{"id":13955,"date":"2025-06-05T18:10:24","date_gmt":"2025-06-05T11:10:24","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=13955"},"modified":"2025-07-03T19:50:04","modified_gmt":"2025-07-03T12:50:04","slug":"cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/","title":{"rendered":"C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng th\u01b0\u1eddng g\u1eb7p"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Su_phan_cuc_cua_ham_la_gi\" >S\u1ef1 ph\u00e2n c\u1ef1c c\u1ee7a h\u00e0m l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Cac_ly_thuyet_lien_quan_den_diem_cuc_doan_cua_ham\" >C\u00e1c l\u00fd thuy\u1ebft li\u00ean quan \u0111\u1ebfn \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Dinh_nghia_gia_tri_toi_da_va_gia_tri_toi_thieu\" >\u0110\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Dinh_ly_ve_dieu_tri_chuc_nang\" >\u0110\u1ecbnh l\u00fd v\u1ec1 \u0111i\u1ec1u tr\u1ecb ch\u1ee9c n\u0103ng<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#So_luong_diem_cuc_cua_ham\" >S\u1ed1 l\u01b0\u1ee3ng \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Cach_tim_diem_cuc_cua_ham\" >C\u00e1ch t\u00ecm \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Tim_chuc_nang_cuc_doan_cua_chuc_nang_cap_2\" >T\u00ecm ch\u1ee9c n\u0103ng c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng c\u1ea5p 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Xac_dinh_diem_cuc_cua_ham_thu_3\" >X\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m th\u1ee9 3<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Cach_tim_mot_duong_thang_thong_qua_hai_diem_cuc_doan_cua_ham_thu_ba\" >C\u00e1ch t\u00ecm m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng th\u00f4ng qua hai \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m th\u1ee9 ba:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Tinh_toan_cuc_cua_ham_cap_4_cung_mot_ham\" >T\u00ednh to\u00e1n c\u1ef1c c\u1ee7a h\u00e0m c\u1ea5p 4 (c\u00f9ng m\u1ed9t h\u00e0m)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Cach_xac_dinh_cuc_cua_ham_luong_giac\" >C\u00e1ch x\u00e1c \u0111\u1ecbnh c\u1ef1c c\u1ee7a h\u00e0m l\u01b0\u1ee3ng gi\u00e1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Xac_dinh_diem_cuc_cua_ham_logarit\" >X\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m logarit<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Cac_loai_bai_tap_de_tim_diem_chuc_nang_chung\" >C\u00e1c lo\u1ea1i b\u00e0i t\u1eadp \u0111\u1ec3 t\u00ecm \u0111i\u1ec3m ch\u1ee9c n\u0103ng chung<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Mau_1_Tim_diem_cuc_doan_cua_ham\" >M\u1eabu 1: T\u00ecm \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Phuong_phap_1\" >Ph\u01b0\u01a1ng ph\u00e1p 1:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Phuong_phap_2\" >Ph\u01b0\u01a1ng ph\u00e1p 2:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Vi_du\" >V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Mau_2_Tim_tham_so_m_sao_cho_ham_dat_den_cuc_diem_tai_mot_diem\" >M\u1eabu 2: T\u00ecm tham s\u1ed1 m sao cho h\u00e0m \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i m\u1ed9t \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Giai_phap\" >Gi\u1ea3i ph\u00e1p:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Vi_du-2\" >V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Mau_3_Doi_so_theo_so_cuc_cua_ham\" >M\u1eabu 3: \u0110\u1ed1i s\u1ed1 theo s\u1ed1 c\u1ef1c c\u1ee7a h\u00e0m<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Doi_voi_cuc_cua_ham_thu_ba\" >\u0110\u1ed1i v\u1edbi c\u1ef1c c\u1ee7a h\u00e0m th\u1ee9 ba<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Doi_voi_cuc_cua_ham_bac_hai\" >\u0110\u1ed1i v\u1edbi c\u1ef1c c\u1ee7a h\u00e0m b\u1eadc hai<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Vi_du-3\" >V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/www.ckconitsha.com\/vn\/cuc-tri-cua-ham-so-la-gi-cach-tim-va-bai-tap-van-dung-thuong-gap\/#Mot_so_bai_tap_cuc_doan_ve_chuc_nang_tu_dong\" >M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u1ef1c \u0111oan v\u1ec1 ch\u1ee9c n\u0103ng t\u1ef1 \u0111\u1ed9ng<\/a><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>T\u1ed1i \u01b0u c\u1ee7a ch\u1ee9c n\u0103ng l\u00e0 m\u1ed9t trong nh\u1eefng ph\u1ea7n quan tr\u1ecdng c\u1ee7a ki\u1ebfn \u200b\u200bth\u1ee9c \u0111\u1ea1i s\u1ed1 \u1edf tr\u01b0\u1eddng trung h\u1ecdc. \u0110\u1ec3 l\u00e0m cho sinh vi\u00ean d\u1ec5 d\u00e0ng n\u1eafm b\u1eaft v\u00e0 \u00e1p d\u1ee5ng ki\u1ebfn \u200b\u200bth\u1ee9c n\u00e0y. Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef \u0111\u00e3 t\u00f3m t\u1eaft t\u1ea5t c\u1ea3 c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 c\u00e1ch t\u00ecm c\u00e1c ch\u1ee9c n\u0103ng chung c\u1ee7a ch\u1ee9c n\u0103ng chung ngay d\u01b0\u1edbi d\u00e2y.<\/p>\n<p>                        Xem t\u1ea5t c\u1ea3<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Su_phan_cuc_cua_ham_la_gi\"><\/span>S\u1ef1 ph\u00e2n c\u1ef1c c\u1ee7a h\u00e0m l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>T\u1ed1i \u01b0u c\u1ee7a h\u00e0m l\u00e0 gi\u00e1 tr\u1ecb l\u00e0m cho ch\u1ee9c n\u0103ng thay \u0111\u1ed5i khi thay \u0111\u1ed5i. Xem x\u00e9t h\u00ecnh h\u1ecdc, c\u1ef1c c\u1ee7a h\u00e0m cho th\u1ea5y kho\u1ea3ng c\u00e1ch t\u1ed1i \u0111a t\u1eeb \u0111i\u1ec3m n\u00e0y sang \u0111i\u1ec3m kh\u00e1c v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. <\/p>\n<p>L\u01b0u \u00fd: Gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u kh\u00f4ng ph\u1ea3i l\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u c\u1ee7a h\u00e0m.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_ly_thuyet_lien_quan_den_diem_cuc_doan_cua_ham\"><\/span>C\u00e1c l\u00fd thuy\u1ebft li\u00ean quan \u0111\u1ebfn \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/1-cuc-tri-cua-ham-so.jpg\" alt=\"L\u00fd thuy\u1ebft v\u1ec1 ch\u1ee9c n\u0103ng c\u1ee7a h\u00e0m. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Dinh_nghia_gia_tri_toi_da_va_gia_tri_toi_thieu\"><\/span>\u0110\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Gi\u1ea3 s\u1eed h\u00e0m F \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean k (k \u2282 \u211d) v\u00e0 x0 \u2208 K.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">X0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111i\u1ec3m t\u1ed1i \u0111a c\u1ee7a h\u00e0m F n\u1ebfu c\u00f3 ph\u1ea1m vi (a; b) k ch\u1ee9a \u0111i\u1ec3m x0 sao cho f (x)<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">X0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111i\u1ec3m t\u1ed1i thi\u1ec3u c\u1ee7a h\u00e0m F n\u1ebfu t\u1ed3n t\u1ea1i m\u1ed9t ph\u1ea1m vi (a; b) k ch\u1ee9a \u0111i\u1ec3m x0 sao cho f (x)&gt; f (x0), \u2200 x \u2208 (a; b)  {x0}. Th\u00ec f (x0) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u c\u1ee7a h\u00e0m f.<\/p>\n<\/li>\n<\/ul>\n<p>M\u1ed9t s\u1ed1 ghi ch\u00fa chung:<\/p>\n<ol>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110i\u1ec3m t\u1ed1i \u0111a (t\u1ed1i thi\u1ec3u) x0 \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111oan. Gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (t\u1ed1i thi\u1ec3u) f (x0) c\u1ee7a h\u00e0m \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 c\u1ef1c \u0111oan. H\u00e0m c\u00f3 th\u1ec3 \u0111\u1ea1t t\u1ed1i \u0111a ho\u1eb7c t\u1ed1i thi\u1ec3u t\u1ea1i nhi\u1ec1u \u0111i\u1ec3m tr\u00ean K.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u00f3i chung, gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (t\u1ed1i thi\u1ec3u) f (x0) kh\u00f4ng ph\u1ea3i l\u00e0 t\u1ed1i \u0111a (t\u1ed1i thi\u1ec3u) c\u1ee7a h\u00e0m f tr\u00ean t\u1eadp k; F (x0) ch\u1ec9 l\u00e0 t\u1ed1i \u0111a (t\u1ed1i thi\u1ec3u) c\u1ee7a h\u00e0m F tr\u00ean ph\u1ea1m vi (a; b) ch\u1ee9a x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu x0 l\u00e0 m\u1ed9t \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m f, \u0111i\u1ec3m (x0; f (x0)) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a bi\u1ec3u \u0111\u1ed3 h\u00e0m f.<\/p>\n<\/li>\n<\/ol>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/2-cuc-tri-cua-ham-so.png\" alt=\"Minh h\u1ecda cho \u0111i\u1ec3m t\u1ed1i \u0111a v\u00e0 t\u1ed1i thi\u1ec3u c\u1ee7a h\u00e0m. (\u1ea2nh: Verbalearn.com)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Dinh_ly_ve_dieu_tri_chuc_nang\"><\/span>\u0110\u1ecbnh l\u00fd v\u1ec1 \u0111i\u1ec1u tr\u1ecb ch\u1ee9c n\u0103ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 1: Gi\u1ea3 s\u1eed h\u00e0m F \u0111\u00e3 \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i \u0111i\u1ec3m x0. Sau \u0111\u00f3, n\u1ebfu F c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i \u0111i\u1ec3m x0 th\u00ec f &#8216;(x0) = 0.<\/p>\n<p dir=\"ltr\">M\u1ed9t s\u1ed1 ghi ch\u00fa chung:<\/p>\n<ol>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110i\u1ec1u ng\u01b0\u1ee3c l\u1ea1i c\u00f3 th\u1ec3 kh\u00f4ng \u0111\u00fang. H\u00e0m f &#8216;c\u00f3 th\u1ec3 l\u00e0 0 t\u1ea1i \u0111i\u1ec3m x0 nh\u01b0ng h\u00e0m f kh\u00f4ng \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i \u0111i\u1ec3m x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">H\u00e0m c\u00f3 th\u1ec3 \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i m\u1ed9t \u0111i\u1ec3m m\u00e0 h\u00e0m kh\u00f4ng c\u00f3 \u0111\u1ea1o h\u00e0m.<\/p>\n<\/li>\n<\/ol>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 2: N\u1ebfu f &#8216;(x) thay \u0111\u1ed5i d\u1ea5u hi\u1ec7u t\u1eeb \u00e2m v\u00e0 d\u01b0\u01a1ng khi x \u0111i qua \u0111i\u1ec3m x0 (theo h\u01b0\u1edbng t\u0103ng), h\u00e0m \u0111\u1ea1t \u0111\u1ebfn m\u1ee9c t\u1ed1i thi\u1ec3u t\u1ea1i x0.<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/3-cuc-tri-cua-ham-so.png\" alt=\"\" width=\"400\" height=\"165\"><\/p>\n<p dir=\"ltr\">N\u1ebfu f &#8216;(x) chuy\u1ec3n \u0111\u1ed5i c\u00e1c d\u1ea5u hi\u1ec7u t\u1eeb d\u01b0\u01a1ng sang \u00e2m khi x \u0111i qua \u0111i\u1ec3m x0 (theo h\u01b0\u1edbng t\u0103ng), h\u00e0m t\u1ed1i \u0111a t\u1ea1i x0.<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/4-cuc-tri-cua-ham-so.png\" alt=\"\" width=\"400\" height=\"158\"><\/p>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 3: Gi\u1ea3 s\u1eed h\u00e0m F c\u00f3 \u0111\u1ea1o h\u00e0m \u0111\u1ea7u ti\u00ean tr\u00ean ph\u1ea1m vi (a; b) ch\u1ee9a \u0111i\u1ec3m x0, f &#8216;(x0) = 0 v\u00e0 f v\u1edbi m\u1ee9c th\u1ee9 c\u1ea5p c\u1ee7a c\u1ea5p \u0111\u1ed9 0 kh\u00e1c t\u1ea1i \u0111i\u1ec3m x0.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu f &#8221; (x0) &lt;0, h\u00e0m F \u0111\u1ea1t t\u1ed1i \u0111a t\u1ea1i \u0111i\u1ec3m x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu f &#8221; (x0)&gt; 0 th\u00ec h\u00e0m F \u0111\u1ea1t t\u1ed1i thi\u1ec3u t\u1ea1i \u0111i\u1ec3m x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu f &#8221; (x0) = 0 th\u00ec ch\u00fang ta kh\u00f4ng th\u1ec3 k\u1ebft lu\u1eadn, c\u1ea7n ph\u1ea3i t\u1ea1o m\u1ed9t b\u1ea3ng bi\u1ebfn ho\u1eb7c b\u1ea3ng ch\u1ee9c n\u0103ng.<\/p>\n<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"So_luong_diem_cuc_cua_ham\"><\/span>S\u1ed1 l\u01b0\u1ee3ng \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>M\u1ed7i d\u1ea1ng ch\u1ee9c n\u0103ng c\u00f3 m\u1ed9t \u0111i\u1ec3m c\u1ef1c \u0111oan kh\u00e1c nhau, k\u1ebft lu\u1eadn c\u00f3 th\u1ec3 l\u00e0: kh\u00f4ng c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111oan, c\u00f3 1 \u0111i\u1ec3m c\u1ef1c \u0111oan trong ph\u01b0\u01a1ng tr\u00ecnh c\u1ea5p 2, c\u00f3 2 \u0111i\u1ec3m c\u1ef1c \u0111oan trong ph\u01b0\u01a1ng tr\u00ecnh c\u1ea5p 3, &#8230;<\/p>\n<p>L\u01b0u \u00fd v\u1edbi c\u00e1c \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m:<\/p>\n<ul>\n<li>\u0110i\u1ec3m t\u1ed1i \u0111a (ho\u1eb7c t\u1ed1i thi\u1ec3u) c\u1ee7a X0 l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111oan. Gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (ho\u1eb7c gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u) F (x0) g\u1ecdi chung l\u00e0 c\u1ef1c \u0111oan. T\u1ea1i 1 \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 \u0111a mmaximum v\u00e0 t\u1ed1i thi\u1ec3u.<\/li>\n<li>Gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (ho\u1eb7c gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u) f (x0) kh\u00f4ng ph\u1ea3i l\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (ho\u1eb7c gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u) c\u1ee7a h\u00e0m F m\u00e0 ch\u1ec9 l\u00e0 gi\u00e1 tr\u1ecb t\u1ed1i \u0111a (ho\u1eb7c gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u) c\u1ee7a h\u00e0m F tr\u00ean ph\u1ea1m vi (a; b) ch\u1ee9a x0.<\/li>\n<li>N\u1ebfu 1 \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a F l\u00e0 x0 th\u00ec \u0111i\u1ec3m (x0; f (x0)) l\u00e0 \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m f.<\/li>\n<\/ul>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cach_tim_diem_cuc_cua_ham\"><\/span>C\u00e1ch t\u00ecm \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">M\u1ed7i ch\u1ee9c n\u0103ng c\u00f3 m\u1ed9t t\u00ednh ch\u1ea5t kh\u00e1c nhau v\u00e0 c\u00e1ch t\u00ecm ki\u1ebfm \u0111i\u1ec1u tr\u1ecb c\u1ef1c \u0111\u1ed9. Ch\u1eb3ng bao l\u00e2u, Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef s\u1ebd gi\u1edbi thi\u1ec7u v\u1edbi b\u1ea1n c\u00e1ch x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng ph\u1ed5 bi\u1ebfn trong c\u00e1c c\u00e2u h\u1ecfi thi.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Tim_chuc_nang_cuc_doan_cua_chuc_nang_cap_2\"><\/span>T\u00ecm ch\u1ee9c n\u0103ng c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng c\u1ea5p 2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u00e0m c\u1ea5p 2 c\u00f3 d\u1ea1ng: y = ax2 + bx + c (a \u2260 0) v\u1edbi mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 d = R. ch\u00fang ta c\u00f3: y &#8216;= 2ax + b.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Y &#8216;thay \u0111\u1ed5i d\u1ea5u hi\u1ec7u khi x v\u01b0\u1ee3t qua x0 = -b\/2a<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">H\u00e0m \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i x0 = -b\/2a<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/5-cuc-tri-cua-ham-so.png\" alt=\"\" width=\"300\" height=\"109\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Xac_dinh_diem_cuc_cua_ham_thu_3\"><\/span>X\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m th\u1ee9 3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u00e0m 3 c\u00f3 bi\u1ec3u m\u1eabu: y = ax3 + bx2 + cx + d (a \u2260 0) v\u1edbi mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 d = r. Ch\u00fang ta c\u00f3: y &#8216;= 3ax2 + 2bx + c \u2192&#8217; = b2 &#8211; 3ac.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0394 &#8216;0: y&#8217; kh\u00f4ng thay \u0111\u1ed5i \u2192 ch\u1ee9c n\u0103ng kh\u00f4ng c\u00f3 th\u00e1i c\u1ef1c<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0394 &#8216;&gt; 0: y&#8217; Thay \u0111\u1ed5i 2 l\u1ea7n \u2192 H\u00e0m c\u00f3 hai th\u00e1i c\u1ef1c (1 CD v\u00e0 1 CT)<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cach_tim_mot_duong_thang_thong_qua_hai_diem_cuc_doan_cua_ham_thu_ba\"><\/span>C\u00e1ch t\u00ecm m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng th\u00f4ng qua hai \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m th\u1ee9 ba:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">Ch\u00fang ta c\u00f3 th\u1ec3 ph\u00e2n t\u00edch: y = f (x) = (ax + b) f &#8216;(x) + cx + d b\u1eb1ng c\u00e1ch chia \u0111a th\u1ee9c f (x) cho \u0111a th\u1ee9c f&#8217; (x).<\/p>\n<p dir=\"ltr\">Gi\u1ea3 s\u1eed ch\u1ee9c n\u0103ng \u0111\u1ea1t \u0111\u1ebfn m\u1ee9c c\u1ef1c \u0111oan t\u1ea1i x1 v\u00e0 x2<\/p>\n<p dir=\"ltr\">Ch\u00fang ta c\u00f3: f (x1) = (ax1 + b) f &#8216;(x1) + cx1 + d \u2192 f (x1) = cx1 + d v\u00ec f&#8217; (x1) = 0<\/p>\n<p dir=\"ltr\">T\u01b0\u01a1ng t\u1ef1: f (x2) = cx2 + d v\u00ec f &#8216;(x2) = 0<\/p>\n<p dir=\"ltr\">K\u1ebft lu\u1eadn: D\u00f2ng qua hai \u0111i\u1ec3m c\u1ef1c \u0111oan c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: y = cx + d<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/cuc-tri-cua-ham-so-01.jpg\" alt=\"L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 t\u00ecm s\u1ef1 c\u1ef1c \u0111oan c\u1ee7a h\u00e0m th\u1ee9 3. (\u1ea2nh: S\u01b0u t\u1ea7m Internet)\" width=\"800\" height=\"427\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Tinh_toan_cuc_cua_ham_cap_4_cung_mot_ham\"><\/span>T\u00ednh to\u00e1n c\u1ef1c c\u1ee7a h\u00e0m c\u1ea5p 4 (c\u00f9ng m\u1ed9t h\u00e0m)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u00e0m ch\u1ee9c n\u0103ng c\u00f3 d\u1ea1ng: y = ax4 + bx2 + c (a \u2260 0) v\u1edbi mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 d = r. Ch\u00fang ta c\u00f3: y &#8216;= 4ax^3 + 2bx = 2x (2ax^2 + b) v\u00e0 y&#8217; = 0 x = 0 2ax^2 + b = 0 x = 0 x62 = -b\/2a.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Khi -B\/2A 0  b\/2a 0, y &#8216;ch\u1ec9 thay \u0111\u1ed5i d\u1ea5u m\u1ed9t l\u1ea7n khi x v\u01b0\u1ee3t qua x0 = 0 \u2192 h\u00e0m \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i XO = 0<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Khi -B\/2A&gt; 0  b\/2a &lt;0, y &#039;thay \u0111\u1ed5i d\u1ea5u hi\u1ec7u 3 l\u1ea7n \u2192 h\u00e0m c\u00f3 3 c\u1ef1c<\/p>\n<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/cuc-tri-cua-ham-so-02.jpg\" alt=\"T\u00ednh to\u00e1n c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng tr\u00f9ng h\u1ee3p. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"800\" height=\"819\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cach_xac_dinh_cuc_cua_ham_luong_giac\"><\/span>C\u00e1ch x\u00e1c \u0111\u1ecbnh c\u1ef1c c\u1ee7a h\u00e0m l\u01b0\u1ee3ng gi\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Ph\u01b0\u01a1ng ph\u00e1p t\u00ecm ki\u1ebfm c\u1ef1c \u0111oan c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c nh\u01b0 sau:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: T\u00ecm mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: T\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m y &#8216;= f&#8217; (x), gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh y &#8216;= 0, gi\u1ea3 s\u1eed gi\u1ea3i ph\u00e1p x = x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 3: L\u00fac \u0111\u00f3 ch\u00fang ta t\u00ecm th\u1ea5y \u0111\u1ea1o h\u00e0m. &#8216; <\/p>\n<\/li>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">T\u00ednh to\u00e1n y &#8221; (x0) v\u00e0 sau \u0111\u00f3 \u0111\u01b0a ra k\u1ebft lu\u1eadn d\u1ef1a tr\u00ean \u0110\u1ecbnh l\u00fd 2.<\/p>\n<\/li>\n<\/ul>\n<\/ul>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Xac_dinh_diem_cuc_cua_ham_logarit\"><\/span>X\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c c\u1ee7a h\u00e0m logarit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Ch\u00fang ta c\u1ea7n l\u00e0m theo c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: T\u00ecm mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: T\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m y &#8216;, sau \u0111\u00f3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh y&#8217; = 0, gi\u1ea3 s\u1eed gi\u1ea3i ph\u00e1p x = x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 3: Xem x\u00e9t hai kh\u1ea3 n\u0103ng:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">T\u00ecm ph\u00e1i sinh y &#8221;.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">T\u00ednh to\u00e1n y &#8221; (x0) v\u00e0 sau \u0111\u00f3 \u0111\u01b0a ra k\u1ebft lu\u1eadn d\u1ef1a tr\u00ean \u0110\u1ecbnh l\u00fd 3.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu b\u1ea1n xem x\u00e9t d\u1ea5u hi\u1ec7u c\u1ee7a y &#8216;: th\u00ec: t\u1ea1o m\u1ed9t b\u1ea3ng bi\u1ebfn v\u00e0 sau \u0111\u00f3 \u0111\u01b0a ra k\u1ebft lu\u1eadn d\u1ef1a tr\u00ean \u0110\u1ecbnh l\u00fd 2.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu b\u1ea1n kh\u00f4ng th\u1ec3 xem x\u00e9t d\u1ea5u hi\u1ec7u c\u1ee7a Y &#8216;: th\u00ec:<\/p>\n<\/li>\n<\/ul>\n<\/ul>\n<table style=\"border-collapse: collapse;width: 100%;background-color: #fbeeb8\" border=\"1\">\n<tr>\n<td style=\"width: 98.5189%\">\n<p style=\"text-align: center\">Gi\u00fap con b\u1ea1n h\u1ecdc to\u00e1n k\u1ebft h\u1ee3p v\u1edbi ti\u1ebfng Anh si\u00eau ti\u1ebft ki\u1ec7m ch\u1ec9 tr\u00ean \u1ee9ng d\u1ee5ng to\u00e1n h\u1ecdc kh\u1ec9. V\u1edbi n\u1ed9i dung gi\u1ea3ng d\u1ea1y v\u1ea1n n\u0103ng \u0111\u1ec3 gi\u00fap tr\u1ebb ph\u00e1t tri\u1ec3n t\u01b0 duy n\u00e3o b\u1ed9 v\u00e0 ng\u00f4n ng\u1eef to\u00e0n di\u1ec7n ch\u1ec9 v\u1edbi kho\u1ea3ng 2k\/ng\u00e0y.<img decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/xemchitiet.png\" alt=\"\" width=\"185\"><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_loai_bai_tap_de_tim_diem_chuc_nang_chung\"><\/span>C\u00e1c lo\u1ea1i b\u00e0i t\u1eadp \u0111\u1ec3 t\u00ecm \u0111i\u1ec3m ch\u1ee9c n\u0103ng chung<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">B\u1edfi v\u00ec c\u00e1c th\u00e1i c\u1ef1c c\u1ee7a c\u00e1c th\u00e1i c\u1ef1c xu\u1ea5t hi\u1ec7n th\u01b0\u1eddng xuy\u00ean trong c\u00e1c c\u00e2u h\u1ecfi thi qu\u1ed1c gia h\u00e0ng n\u0103m. N\u1eafm b\u1eaft t\u00ecnh hu\u1ed1ng chung, Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef \u0111\u00e3 t\u00f3m t\u1eaft ba lo\u1ea1i v\u1ea5n \u0111\u1ec1 ph\u1ed5 bi\u1ebfn li\u00ean quan \u0111\u1ebfn c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng, gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng th\u1ef1c h\u00e0nh h\u01a1n.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_1_Tim_diem_cuc_doan_cua_ham\"><\/span>M\u1eabu 1: T\u00ecm \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">C\u00f3 2 c\u00e1ch \u0111\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 t\u00ecm c\u00e1c \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m, b\u1ea1n c\u00f3 th\u1ec3 l\u00e0m theo ngay b\u00ean d\u01b0\u1edbi.<\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Phuong_phap_1\"><\/span>Ph\u01b0\u01a1ng ph\u00e1p 1:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: T\u00ecm t\u1eadp h\u1ee3p x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: T\u00ednh f &#8216;(x). T\u00ecm c\u00e1c \u0111i\u1ec3m t\u1ea1i f &#8216;(x) b\u1eb1ng 0 ho\u1eb7c f&#8217; (x) v\u00f4 th\u1eddi h\u1ea1n.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 3: T\u1ea1o m\u1ed9t b\u1ea3ng bi\u1ebfn.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 4: T\u1eeb b\u1ea3ng bi\u1ebfn, c\u00e1c \u0111i\u1ec3m c\u1ef1c \u0111oan.<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Phuong_phap_2\"><\/span>Ph\u01b0\u01a1ng ph\u00e1p 2:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: T\u00ecm t\u1eadp h\u1ee3p x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: T\u00ednh f &#8216;(x). Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh f &#8216;(x) v\u00e0 k\u00fd hi\u1ec7u XI (i = 1,2,3, &#8230;) l\u00e0 c\u00e1c gi\u1ea3i ph\u00e1p c\u1ee7a n\u00f3.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 3: T\u00ednh f &#8221; (x) v\u00e0 f &#8221; (xi).<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 4: D\u1ef1a tr\u00ean d\u1ea5u hi\u1ec7u c\u1ee7a f &#8221; (xi) suy ra c\u00e1c thu\u1ed9c t\u00ednh c\u1ef1c \u0111oan c\u1ee7a \u0111i\u1ec3m XI.<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span><em>V\u00ed d\u1ee5:<\/em><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\"><em>T\u00ecm c\u1ef1c c\u1ee7a h\u00e0m y = 2&#215;3 &#8211; 6x + 2.<\/em><\/p>\n<p dir=\"ltr\"><em>H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/em><\/p>\n<p dir=\"ltr\"><em>T\u1eadp h\u1ee3p x\u00e1c \u0111\u1ecbnh d = R.<\/em><\/p>\n<p dir=\"ltr\"><em>T\u00ednh y &#8216;= 6x^2 &#8211; 6. \u0110\u1eb7t y&#8217; = 0 \u21d4 6&#215;2 &#8211; 6 = 0 x = \u00b1 1.<\/em><\/p>\n<p dir=\"ltr\">B\u1ea3ng bi\u1ebfn:<\/p>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/7-cuc-tri-cua-ham-so.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\"><em>V\u00ec v\u1eady, h\u00e0m \u0111\u1ea1t t\u1ed1i \u0111a t\u1ea1i x = &#8211; 1, y = 6 v\u00e0 h\u00e0m \u0111\u1ea1t m\u1ee9c t\u1ed1i thi\u1ec3u t\u1ea1i x = 1, y = -2.<\/em><\/p>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/8-cuc-tri-cua-ham-so.jpg\" alt=\"M\u1ed9t s\u1ed1 lo\u1ea1i b\u00e0i t\u1eadp v\u1ec1 c\u1ef1c k\u1ef3 c\u1ee7a ch\u1ee9c n\u0103ng chung. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_2_Tim_tham_so_m_sao_cho_ham_dat_den_cuc_diem_tai_mot_diem\"><\/span>M\u1eabu 2: T\u00ecm tham s\u1ed1 m sao cho h\u00e0m \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i m\u1ed9t \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Giai_phap\"><\/span>Gi\u1ea3i ph\u00e1p:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">Trong h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y, ch\u00fang t\u00f4i ch\u1ec9 xem x\u00e9t tr\u01b0\u1eddng h\u1ee3p h\u00e0m ph\u00e1i sinh t\u1ea1i x0. V\u00e0o th\u1eddi \u0111i\u1ec3m \u0111\u00f3, \u0111\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 n\u00e0y, ch\u00fang t\u00f4i th\u1ef1c hi\u1ec7n hai b\u01b0\u1edbc.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: \u0110i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft \u0111\u1ec3 h\u00e0m \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i x0 l\u00e0 y &#8216;(x0) = 0, t\u1eeb \u0111i\u1ec1u ki\u1ec7n n\u00e0y, ch\u00fang t\u00f4i t\u00ecm th\u1ea5y gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: Ki\u1ec3m tra b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng m\u1ed9t trong hai quy t\u1eafc c\u1ef1c \u0111oan, \u0111\u1ec3 xem x\u00e9t li\u1ec7u gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1 v\u1eeba \u0111\u01b0\u1ee3c th\u1ecfa m\u00e3n th\u1ecfa m\u00e3n c\u00e1c y\u00eau c\u1ea7u c\u1ee7a v\u1ea5n \u0111\u1ec1?<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Vi_du-2\"><\/span><em>V\u00ed d\u1ee5:<\/em><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\"><em>Cho h\u00e0m y = x^3 &#8211; 3mx^2 + (m^2 &#8211; 1) x + 2, m l\u00e0 m\u1ed9t tham s\u1ed1 th\u1ef1c. T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m sao cho h\u00e0m \u0111\u00e3 \u0111\u1ea1t \u0111\u1ebfn m\u1ee9c t\u1ed1i thi\u1ec3u t\u1ea1i x = 2.<\/em><\/p>\n<p dir=\"ltr\"><em>H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/em><\/p>\n<p dir=\"ltr\"><em>T\u1eadp h\u1ee3p x\u00e1c \u0111\u1ecbnh d = R. T\u00ednh y &#8216;= 3x^2 &#8211; 6mx + m^2 &#8211; 1; y &#8221; = 6x &#8211; 6m.<\/em><\/p>\n<p dir=\"ltr\"><em>H\u00e0m \u0111\u01b0\u1ee3c \u0111\u01b0a ra t\u1ed1i thi\u1ec3u t\u1ea1i x = 2 \u2192 <\/em><\/p>\n<p dir=\"ltr\"><em><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/9-cuc-tri-cua-ham-so.png\" alt=\"\" width=\"300\" height=\"54\"><\/em><\/p>\n<p dir=\"ltr\"><em>M = 1.<\/em><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_3_Doi_so_theo_so_cuc_cua_ham\"><\/span>M\u1eabu 3: \u0110\u1ed1i s\u1ed1 theo s\u1ed1 c\u1ef1c c\u1ee7a h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Doi_voi_cuc_cua_ham_thu_ba\"><\/span>\u0110\u1ed1i v\u1edbi c\u1ef1c c\u1ee7a h\u00e0m th\u1ee9 ba<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">\u0110\u1eb7t h\u00e0m y = ax^3 + bx^2 + cx + d, a \u2260 0. V\u00e0o th\u1eddi \u0111i\u1ec3m \u0111\u00f3, ch\u00fang ta c\u00f3: y &#8216;= 0 3ax^2 + 2bx + c = 0 (1); &#8221;Y &#8216;= B^2 &#8211; 3ac.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Ph\u01b0\u01a1ng tr\u00ecnh (1) C\u00e1c gi\u1ea3i ph\u00e1p v\u00f4 h\u00ecnh ho\u1eb7c \u0111\u00f4i, h\u00e0m \u0111\u01b0\u1ee3c \u0111\u01b0a ra kh\u00f4ng c\u00f3 th\u00e1i c\u1ef1c.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Ch\u1ee9c n\u0103ng 3 kh\u00f4ng c\u00f3 c\u1ef1c \u0111oan \u21d4 b^2 &#8211; 3ac \u2264 0<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai gi\u1ea3i ph\u00e1p ri\u00eang bi\u1ec7t, h\u00e0m \u0111\u01b0\u1ee3c \u0111\u01b0a ra c\u00f3 2 th\u00e1i c\u1ef1c.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">H\u00e0m 3 c\u00f3 2 c\u1ef1c \u21d4 b^2 &#8211; 3ac&gt; 0<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Doi_voi_cuc_cua_ham_bac_hai\"><\/span>\u0110\u1ed1i v\u1edbi c\u1ef1c c\u1ee7a h\u00e0m b\u1eadc hai<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">Cho h\u00e0m: y = ax^4 + bx^2 + c (a \u2260 0) c\u00f3 bi\u1ec3u \u0111\u1ed3 (c). V\u00e0o th\u1eddi \u0111i\u1ec3m \u0111\u00f3, ch\u00fang ta c\u00f3: y &#8216;= 4ax^3 + 2bx; y &#8216;= 0 x = 0 ho\u1eb7c x^2 = -b\/2a.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">.<\/p>\n<\/li>\n<\/ul>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Vi_du-3\"><\/span><em>V\u00ed d\u1ee5:<\/em><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\"><em>T\u00ecm m sao cho h\u00e0m y = x3 + mx + 2 c\u00f3 c\u1ea3 t\u1ed1i \u0111a v\u00e0 t\u1ed1i thi\u1ec3u.<\/em><\/p>\n<p dir=\"ltr\"><em>H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/em><\/p>\n<p dir=\"ltr\"><em>Ch\u00fang ta c\u00f3: y &#8216;= 3&#215;2 + m \u2192 h\u00e0m y = x3 + mx + 2 c\u00f3 c\u1ea3 t\u1ed1i \u0111a v\u00e0 t\u1ed1i thi\u1ec3u khi v\u00e0 ch\u1ec9 khi y&#8217; = 0 c\u00f3 hai gi\u1ea3i ph\u00e1p ri\u00eang bi\u1ec7t. V\u00ec v\u1eady, m &lt;0.<\/em><\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mot_so_bai_tap_cuc_doan_ve_chuc_nang_tu_dong\"><\/span>M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u1ef1c \u0111oan v\u1ec1 ch\u1ee9c n\u0103ng t\u1ef1 \u0111\u1ed9ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/10-cuc-tri-cua-ham-so.jpg\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">C\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a c\u00e1c b\u00e0i t\u1eadp tr\u00ean l\u00e0: 1a; 2d; 3a; 4A; 5A; 6a; 7d; 8d; 9d; 10b; 11c.<\/p>\n<p dir=\"ltr\">Tr\u00ean \u0111\u00e2y l\u00e0 t\u1ea5t c\u1ea3 ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng m\u00e0 Kh\u1ec9 mu\u1ed1n chia s\u1ebb v\u1edbi \u0111\u1ed9c gi\u1ea3. Hy v\u1ecdng b\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u00fap b\u1ea1n xem x\u00e9t m\u1ed9t ph\u1ea7n cho c\u00e1c k\u1ef3 thi s\u1eafp t\u1edbi. Xin vui l\u00f2ng \u0111i c\u00f9ng b\u1ea1n!<\/p>\n<p>Ngu\u1ed3n: <a href=\"https:\/\/www.ckconitsha.com\/vn\/\">https:\/\/www.ckconitsha.com\/vn\/<\/a> T\u00e1c gi\u1ea3: <a href=\"https:\/\/www.ckconitsha.com\/vn\/author\/nguyenlandung\">Nguy\u1ec5n L\u00e2n d\u0169ng<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u1ed1i \u01b0u c\u1ee7a ch\u1ee9c n\u0103ng l\u00e0 m\u1ed9t trong nh\u1eefng ph\u1ea7n quan tr\u1ecdng c\u1ee7a ki\u1ebfn \u200b\u200bth\u1ee9c \u0111\u1ea1i s\u1ed1 \u1edf tr\u01b0\u1eddng trung h\u1ecdc. \u0110\u1ec3 l\u00e0m cho sinh vi\u00ean d\u1ec5 d\u00e0ng n\u1eafm b\u1eaft v\u00e0 \u00e1p d\u1ee5ng ki\u1ebfn \u200b\u200bth\u1ee9c n\u00e0y. Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef \u0111\u00e3 t\u00f3m t\u1eaft t\u1ea5t c\u1ea3 c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 c\u00e1ch t\u00ecm c\u00e1c&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[100],"tags":[],"class_list":["post-13955","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/comments?post=13955"}],"version-history":[{"count":2,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13955\/revisions"}],"predecessor-version":[{"id":16731,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13955\/revisions\/16731"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=13955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=13955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=13955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}