{"id":21546,"date":"2025-07-08T14:40:52","date_gmt":"2025-07-08T07:40:52","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=21546"},"modified":"2025-07-08T14:40:52","modified_gmt":"2025-07-08T07:40:52","slug":"dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/","title":{"rendered":"\u0110\u1ecbnh ngh\u0129a h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn &amp; c\u00e1ch gi\u1ea3i b\u00e0i t\u1eadp chi ti\u1ebft"},"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\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Tong_quan_ve_cac_chuc_nang_quan_ly\" >T\u1ed5ng quan v\u1ec1 c\u00e1c ch\u1ee9c n\u0103ng qu\u1ea3n l\u00fd<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Chuc_nang_la_gi\" >Ch\u1ee9c n\u0103ng l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Ham_Codia_la_gi\" >H\u00e0m Codia l\u00e0 g\u00ec?<\/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\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Khi_nao_ma_cua_ma\" >Khi n\u00e0o m\u00e3 c\u1ee7a m\u00e3?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Cac_loai_van_de_ve_cung_mot_chuc_nang_bien_trong_cac_khoang_thoi_gian_chung\" >C\u00e1c lo\u1ea1i v\u1ea5n \u0111\u1ec1 v\u1ec1 c\u00f9ng m\u1ed9t ch\u1ee9c n\u0103ng bi\u1ebfn trong c\u00e1c kho\u1ea3ng th\u1eddi gian chung<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mau_1_Tim_m_sao_cho_chuc_nang_cua_cung_mot_bien_tren_r\" >M\u1eabu 1: T\u00ecm m sao cho ch\u1ee9c n\u0103ng c\u1ee7a c\u00f9ng m\u1ed9t bi\u1ebfn tr\u00ean r<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mau_2_Tim_M_sao_cho_ham_dong_nhat_va_nghich_dao_tren_moi_khoang_thoi_gian_duoc_chi_dinh\" >M\u1eabu 2: T\u00ecm M sao cho h\u00e0m \u0111\u1ed3ng nh\u1ea5t v\u00e0 ngh\u1ecbch \u0111\u1ea3o tr\u00ean m\u1ed7i kho\u1ea3ng th\u1eddi gian \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh<\/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\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mau_3_Thu_nghiem_tinh_than_cua_dao_ham\" >M\u1eabu 3: Th\u1eed nghi\u1ec7m tinh th\u1ea7n c\u1ee7a \u0111\u1ea1o h\u00e0m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mau_4_Tham_so_phan_lap_m\" >M\u1eabu 4: Tham s\u1ed1 ph\u00e2n l\u1eadp m<\/a><\/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\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mau_5_Ham_tuyen_tinh_don_dieu_tren_pham_vi_da_cho\" >M\u1eabu 5: H\u00e0m tuy\u1ebfn t\u00ednh \u0111\u01a1n \u0111i\u1ec7u tr\u00ean ph\u1ea1m vi \u0111\u00e3 cho<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Cac_bai_tap_chuc_nang_tu_dong\" >C\u00e1c b\u00e0i t\u1eadp ch\u1ee9c n\u0103ng t\u1ef1 \u0111\u1ed9ng<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.ckconitsha.com\/vn\/dinh-nghia-ham-so-dong-bien-cach-giai-bai-tap-chi-tiet\/#Mot_so_meo_de_tinh_toan_cac_bai_tap_toan_hoc_kiem_tra_nhanh\" >M\u1ed9t s\u1ed1 m\u1eb9o \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c b\u00e0i t\u1eadp to\u00e1n h\u1ecdc ki\u1ec3m tra nhanh<\/a><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>Khi n\u00e0o m\u00e3 c\u1ee7a m\u00e3? \u0110\u00e2y c\u00f3 l\u1ebd l\u00e0 m\u1ed9t c\u00e2u h\u1ecfi khi\u1ebfn nhi\u1ec1u sinh vi\u00ean hoang mang khi g\u1eb7p ph\u1ea3i. \u0110\u1eebng lo l\u1eafng! Trong b\u00e0i vi\u1ebft n\u00e0y, Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef s\u1ebd gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng h\u00f3a to\u00e0n b\u1ed9 ki\u1ebfn \u200b\u200bth\u1ee9c c\u1ee7a Li\u00ean minh. H\u00e3y ch\u00fa \u00fd v\u00e0 \u0111\u1eebng b\u1ecf l\u1ee1 th\u00f4ng tin d\u01b0\u1edbi \u0111\u00e2y!<\/p>\n<p>                                    <img decoding=\"async\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/image\/600x480.png\"><\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Tong_quan_ve_cac_chuc_nang_quan_ly\"><\/span>T\u1ed5ng quan v\u1ec1 c\u00e1c ch\u1ee9c n\u0103ng qu\u1ea3n l\u00fd<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Khi h\u1ecdc \u1edf tr\u01b0\u1eddng tr\u01b0\u1edbc khi h\u1ecdc m\u1ed9t v\u1ea5n \u0111\u1ec1 m\u1edbi. Ch\u00fang t\u00f4i th\u01b0\u1eddng \u0111\u01b0\u1ee3c ban cho ng\u01b0\u1eddi quen v\u1edbi kh\u00e1i ni\u1ec7m v\u00e0 \u0111\u1ecbnh ngh\u0129a. M\u1ed9t khi ch\u00fang ta \u0111\u00e3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft, ch\u00fang ta \u00e1p d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i t\u1eadp. V\u00ec v\u1eady, tr\u01b0\u1edbc ti\u00ean \u0111\u1ec3 nghi\u00ean c\u1ee9u t\u1ed1t v\u1ec1 ch\u1ee9c n\u0103ng c\u1ee7a bi\u1ebfn b\u1ea1n c\u1ea7n \u0111\u1ec3 hi\u1ec3u ch\u1ee9c n\u0103ng l\u00e0 g\u00ec?<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Chuc_nang_la_gi\"><\/span>Ch\u1ee9c n\u0103ng l\u00e0 g\u00ec? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Hi\u1ec3u theo c\u00e1ch tr\u1ef1c quan nh\u1ea5t, h\u00e0m \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t qu\u00e1 tr\u00ecnh li\u00ean k\u1ebft c\u00e1c ph\u00e2n t\u1eed c\u1ee7a t\u1eadp ch\u00ednh X v\u1edbi m\u1ed9t ph\u1ea7n t\u1eed nh\u1ea5t \u0111\u1ecbnh trong b\u1ed9 s\u01b0u t\u1eadp Y.<\/p>\n<p dir=\"ltr\">V\u1ec1 m\u1eb7t ch\u00ednh th\u1ee9c, \u0111\u1ed1i v\u1edbi m\u1ed9t h\u00e0m F t\u1eeb t\u1eadp X \u0111\u1ebfn y th\u1ef1c h\u00e0nh theo t\u1eadp G. bao g\u1ed3m c\u00e1c c\u1eb7p th\u1ee9 t\u1ef1 (x, y) v\u00e0 x thu\u1ed9c X, Y thu\u1ed9c v\u1ec1 Y. C\u00f3 th\u1ec3 hi\u1ec3u theo m\u1ed9t c\u00e1ch kh\u00e1c, v\u1edbi t\u1ea5t c\u1ea3 X trong X s\u1ebd c\u00f3 m\u1ed9t ph\u1ea7n ch\u00ednh x\u00e1c c\u1ee7a Y. v\u00e0 c\u1eb7p (X, Y)<\/p>\n<p dir=\"ltr\">Gi\u1ea3 s\u1eed thu th\u1eadp g \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m. V\u1ec1 h\u00ecnh th\u1ee9c, t\u1eadp th\u1ec3 d\u1ee5c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi h\u00e0m tr\u00ean. \u0110\u1ed3ng th\u1eddi, h\u00e0m th\u01b0\u1eddng \u0111\u01b0\u1ee3c ph\u00e2n bi\u1ec7t v\u1edbi bi\u1ec3u \u0111\u1ed3 c\u1ee7a ch\u00ednh n\u00f3.<\/p>\n<p dir=\"ltr\">Ngo\u00e0i ra, ch\u1ee9c n\u0103ng c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u00e1nh x\u1ea1, m\u1eb7c d\u00f9 c\u00f3 m\u1ed9t s\u1ed1 gi\u1ea3 thuy\u1ebft ri\u00eang bi\u1ec7t gi\u1eefa h\u00e0m v\u00e0 \u00e1nh x\u1ea1. \u0110\u1ed1i v\u1edbi \u0111\u1ecbnh ngh\u0129a c\u1ee7a h\u00e0m, x v\u00e0 y s\u1ebd \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1eadp h\u1ee3p v\u00e0 mi\u1ec1n \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh. N\u1ebfu (x, y) c\u1ee7a c\u00f9ng m\u1ed9t b\u1ed9 thu th\u1eadp F, th\u00ec y s\u1ebd l\u00e0 h\u00ecnh \u1ea3nh c\u1ee7a x \u0111\u1ebfn f. Ho\u1eb7c ng\u01b0\u1ee3c l\u1ea1i gi\u00e1 tr\u1ecb c\u1ee7a F c\u0169ng s\u1ebd \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cho \u0111\u1ed1i s\u1ed1 c\u1ee7a X. <\/p>\n<p dir=\"ltr\">C\u1ee5 th\u1ec3 h\u01a1n, v\u1edbi b\u1ed1i c\u1ea3nh c\u1ee7a c\u00e1c s\u1ed1, y s\u1ebd l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a f cho gi\u00e1 tr\u1ecb x. N\u00f3i t\u00f3m l\u1ea1i, y s\u1ebd l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a x v\u00e0 \u0111\u01b0\u1ee3c t\u01b0\u1ee3ng tr\u01b0ng l\u00e0 y = f (x).<\/p>\n<p dir=\"ltr\">N\u1ebfu mi\u1ec1n v\u00e0 mi\u1ec1n thu th\u1eadp c\u1ee7a F v\u00e0 G gi\u1ed1ng nhau, ch\u00fang t\u00f4i s\u1ebd n\u00f3i r\u1eb1ng c\u00e1c ch\u1ee9c n\u0103ng F v\u00e0 G s\u1ebd b\u1eb1ng nhau. C\u1ee5 th\u1ec3 f = g n\u1ebfu f (x) = g (x) v\u1edbi x thu\u1ed9c v\u1ec1 x, trong \u0111\u00f3 f: x \u2192 y v\u00e0 g: x \u2192 y.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Ham_Codia_la_gi\"><\/span>H\u00e0m Codia l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u00e0m bi\u1ebfn l\u00e0 h\u00e0m v\u1edbi x v\u00e0 f (x) \u0111\u1ec3 gi\u1ea3m ho\u1eb7c t\u0103ng c\u00f9ng nhau. Ng\u01b0\u1ee3c l\u1ea1i, h\u00e0m ngh\u1ecbch \u0111\u1ea3o l\u00e0 h\u00e0m m\u00e0 n\u1ebfu x gi\u1ea3m, f (x) t\u0103ng v\u00e0 x t\u0103ng, th\u00ec F (x) gi\u1ea3m.<\/p>\n<p dir=\"ltr\" style=\"font-size: medium;font-weight: 400\">Gi\u1ea3 s\u1eed k l\u00e0 m\u1ed9t ph\u1ea1m vi, m\u1ed9t n\u1eeda ho\u1eb7c m\u1ed9t \u0111o\u1ea1n v\u0103n v\u00e0 h\u00e0m y = f (x) l\u00e0 m\u1ed9t h\u00e0m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean K. Ch\u00fang ta c\u00f3 h\u00e0m y = f (x) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 bi\u1ebfn ho\u1eb7c t\u0103ng tr\u00ean k, n\u1ebfu: v\u1edbi t\u1ea5t c\u1ea3 x1, x2 thu\u1ed9c K m\u00e0 x1<\/p>\n<p dir=\"ltr\" style=\"font-size: medium;font-weight: 400\">Hi\u1ec7u su\u1ea5t bi\u1ec3u \u0111\u1ed3 c\u1ee7a ch\u1ee9c n\u0103ng n\u00e0y l\u00e0 m\u1ed9t c\u00e1ch l\u00ean. Khi h\u00e0m ngh\u1ecbch \u0111\u1ea3o ho\u1eb7c \u0111\u1ed3ng ph\u1ea1m, n\u00f3 c\u0169ng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m \u0111\u01a1n \u0111i\u1ec7u tr\u00ean K.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Khi_nao_ma_cua_ma\"><\/span>Khi n\u00e0o m\u00e3 c\u1ee7a m\u00e3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110i\u1ec1u ki\u1ec7n cho ch\u1ee9c n\u0103ng c\u1ee7a c\u00f9ng m\u1ed9t bi\u1ebfn tr\u00ean k l\u00e0 khi:<\/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\/1-ham-so-dong-bien.png\" alt=\"\" width=\"300\" height=\"69\"><\/p>\n<p dir=\"ltr\">\u0110\u01b0a ra m\u1ed9t h\u00e0m f \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 c\u00f3 \u0111\u1ea1o h\u00e0m tr\u00ean K. N\u1ebfu f &#039;(x)&gt; 0 cho t\u1ea5t c\u1ea3 x thu\u1ed9c v\u1ec1 K, h\u00e0m s\u1ebd \u0111\u1ed3ng nh\u1ea5t tr\u00ean K. do \u0111\u00f3 b\u1ea1n c\u00f3 th\u1ec3 bi\u1ebft khi n\u00e0o ch\u1ee9c n\u0103ng c\u1ee7a \u0111\u1ed3ng nh\u1ea5t l\u00e0 v\u00e0 \u0111i\u1ec1u ki\u1ec7n n\u00e0o l\u00e0 c\u1ea7n thi\u1ebft. \u0110\u1ed3ng th\u1eddi, n\u00f3 c\u0169ng l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft v\u00e0 \u0111\u1ee7 cho m\u1ed9t ch\u1ee9c n\u0103ng \u0111\u01a1n \u0111i\u1ec7u. <\/p>\n<p dir=\"ltr\">\u0110\u1ec3 ng\u01b0\u1eddi \u0111\u1ecdc hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 v\u1ea5n \u0111\u1ec1 n\u00e0y, ch\u00fang ta h\u00e3y t\u00ecm hi\u1ec3u c\u00e1c v\u00ed d\u1ee5 sau: H\u00e3y xem x\u00e9t t\u00ednh ng\u01b0\u1ee3c l\u1ea1i v\u00e0 t\u00ednh \u0111\u1ed3ng nh\u1ea5t c\u1ee7a h\u00e0m, d\u1ef1a tr\u00ean b\u1ea3ng \u0111\u1ec3 t\u00ecm ch\u1ee9c n\u0103ng c\u1ee7a c\u00f9ng m\u1ed9t ph\u1ea1m vi?<\/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\/02-ham-so-dong-bien.gif\" alt=\"\" width=\"200\" height=\"40\"><\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\">Ch\u00fang ta c\u00f3 m\u1ed9t t\u1eadp h\u1ee3p x\u00e1c \u0111\u1ecbnh d = r v\u00e0 y &#039;= 3 &#8211; 2x; \u0110\u1eb7t y &#039;= 0 3 &#8211; 2x = 0 x = 3\/2<\/p>\n<p dir=\"ltr\">\u0110\u01b0\u1ee3c suy ra khi x = 3\/2 sau \u0111\u00f3 y = 25\/4<\/p>\n<p dir=\"ltr\">Ch\u00fang t\u00f4i c\u00f3 b\u1ea3ng bi\u1ebfn sau:<\/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-ham-so-dong-bien.png\" alt=\"\" width=\"400\" height=\"164\"><\/p>\n<p dir=\"ltr\">Th\u00f4ng qua b\u1ea3ng tr\u00ean, b\u1ea1n c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh h\u00e0m ho\u1ea1t \u0111\u1ed9ng tr\u00ean ph\u1ea1m vi t\u1eeb v\u00f4 c\u1ef1c \u0111\u1ebfn 25\/4.<\/p>\n<p dir=\"ltr\">\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_loai_van_de_ve_cung_mot_chuc_nang_bien_trong_cac_khoang_thoi_gian_chung\"><\/span>C\u00e1c lo\u1ea1i v\u1ea5n \u0111\u1ec1 v\u1ec1 c\u00f9ng m\u1ed9t ch\u1ee9c n\u0103ng bi\u1ebfn trong c\u00e1c kho\u1ea3ng th\u1eddi gian chung<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 ki\u1ebfn \u200b\u200bth\u1ee9c c\u1ee7a c\u00f9ng m\u1ed9t ch\u1ee9c n\u0103ng bi\u1ebfn. \u1ede \u0111\u00e2y ch\u00fang t\u00f4i s\u1ebd c\u00f9ng nhau t\u00ecm hi\u1ec3u 5 lo\u1ea1i b\u00e0i t\u1eadp v\u1ec1 c\u00e1c ch\u1ee9c n\u0103ng t\u01b0\u01a1ng t\u1ef1 trong c\u00e1c kho\u1ea3ng th\u1eddi gian.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_1_Tim_m_sao_cho_chuc_nang_cua_cung_mot_bien_tren_r\"><\/span>M\u1eabu 1: T\u00ecm m sao cho ch\u1ee9c n\u0103ng c\u1ee7a c\u00f9ng m\u1ed9t bi\u1ebfn tr\u00ean r<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ed1i v\u1edbi h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y, b\u1ea1n s\u1ebd quen thu\u1ed9c v\u1edbi \u0111a th\u1ee9c th\u1ee9 ba. Ch\u00fang t\u00f4i s\u1ebd c\u00f3 c\u00f4ng th\u1ee9c sau:<\/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\/4-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng:<\/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\/5-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_2_Tim_M_sao_cho_ham_dong_nhat_va_nghich_dao_tren_moi_khoang_thoi_gian_duoc_chi_dinh\"><\/span>M\u1eabu 2: T\u00ecm M sao cho h\u00e0m \u0111\u1ed3ng nh\u1ea5t v\u00e0 ngh\u1ecbch \u0111\u1ea3o tr\u00ean m\u1ed7i kho\u1ea3ng th\u1eddi gian \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">V\u1edbi h\u00ecnh th\u1ee9c t\u00ecm ki\u1ebfm to\u00e1n h\u1ecdc M, c\u00f9ng m\u1ed9t h\u00e0m bi\u1ebfn, ch\u00fang ta s\u1ebd ph\u1ed5 bi\u1ebfn trong h\u00e0m tuy\u1ebfn t\u00ednh, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m ph\u00e2n s\u1ed1 \u0111\u1ea7u ti\u00ean.<\/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\/6-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng:<\/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-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_3_Thu_nghiem_tinh_than_cua_dao_ham\"><\/span>M\u1eabu 3: Th\u1eed nghi\u1ec7m tinh th\u1ea7n c\u1ee7a \u0111\u1ea1o h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">B\u00e0i t\u1eadp: Cho h\u00e0m y = x\u00b3- (m + 1) x\u00b2- (m\u00b2-2m) x + 2020. T\u00ecm M sao cho h\u00e0m ngh\u1ecbch \u0111\u1ea3o tr\u00ean ph\u1ea1m vi (0; 1).<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/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\/08-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_4_Tham_so_phan_lap_m\"><\/span>M\u1eabu 4: Tham s\u1ed1 ph\u00e2n l\u1eadp m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng:<\/p>\n<p dir=\"ltr\">Cho m\u1ed9t h\u00e0m y = x\u00b3 + mx\u00b2 + 2mx + 3. T\u00ecm \u0111i\u1ec1u ki\u1ec7n c\u1ee7a m sao cho h\u00e0m lu\u00f4n thay \u0111\u1ed5i tr\u00ean ph\u1ea1m vi (0; 2).<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/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\/9-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_5_Ham_tuyen_tinh_don_dieu_tren_pham_vi_da_cho\"><\/span>M\u1eabu 5: H\u00e0m tuy\u1ebfn t\u00ednh \u0111\u01a1n \u0111i\u1ec7u tr\u00ean ph\u1ea1m vi \u0111\u00e3 cho<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">N\u1ebfu h\u00e0m tuy\u1ebfn t\u00ednh c\u00f3 c\u00e1c tham s\u1ed1, ch\u1ee9c n\u0103ng c\u1ee7a s\u1ef1 th\u1ea5t b\u1ea1i r\u1ea5t c\u00f3 th\u1ec3 x\u1ea3y ra. Ch\u00fang ta c\u1ea7n xem x\u00e9t tr\u01b0\u1eddng h\u1ee3p c\u1ee7a h\u00e0m bi\u1ebfn th\u00e0nh h\u00e0m \u0111\u1ea7u ti\u00ean. C\u00f4ng th\u1ee9c x\u00e1c \u0111\u1ecbnh \u0111\u1ec3 xem x\u00e9t m\u1ed9t ch\u1ee9c n\u0103ng c\u1ee7a c\u00e1c thay \u0111\u1ed5i nh\u01b0 sau:<\/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\/10-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng:<\/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\/11-ham-so-dong-bien.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">Xem th\u00eam: \u0110\u1ea1o h\u00e0m l\u00e0 g\u00ec? Kh\u00e1i ni\u1ec7m v\u00e0 c\u00f4ng th\u1ee9c t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao<\/p>\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.<\/p>\n<p style=\"text-align: center\">\n<p><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\/timhieungay.png\" alt=\"\" width=\"185\" height=\"38\"><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_bai_tap_chuc_nang_tu_dong\"><\/span>C\u00e1c b\u00e0i t\u1eadp ch\u1ee9c n\u0103ng t\u1ef1 \u0111\u1ed9ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Sau khi bi\u1ebft l\u00fd thuy\u1ebft, nh\u1eefng \u0111i\u1ec1u sau \u0111\u00e2y s\u1ebd l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ec3 h\u1ecdc sinh th\u1ef1c h\u00e0nh nhi\u1ec1u h\u01a1n:<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/ham-so-dong-bien-a.jpg\" alt=\"(Ngu\u1ed3n: T\u00f3m t\u1eaft)\" width=\"100%\"><\/p>\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\u1ea3i ph\u00e1p n\u00e0y gi\u00fap tr\u1ebb ph\u00e1t tri\u1ec3n t\u01b0 duy v\u00e0 ng\u00f4n ng\u1eef to\u00e0n di\u1ec7n v\u1edbi c\u00e1c s\u1ea3n ph\u1ea9m to\u00e1n h\u1ecdc + Vi\u1ec7t Nam + ti\u1ebfng Anh v\u1edbi gi\u1ea3m gi\u00e1 t\u1edbi 50% ng\u00e0y h\u00f4m nay.<\/p>\n<p style=\"text-align: center\">\n<p><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia.monkeyuni.net\/upload\/web\/img\/button_dang-ky-ngay-1.png\" alt=\"\" width=\"185\" height=\"25\"><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mot_so_meo_de_tinh_toan_cac_bai_tap_toan_hoc_kiem_tra_nhanh\"><\/span>M\u1ed9t s\u1ed1 m\u1eb9o \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c b\u00e0i t\u1eadp to\u00e1n h\u1ecdc ki\u1ec3m tra nhanh<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Khi gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp to\u00e1n \u0111\u1eb7c bi\u1ec7t v\u1edbi c\u00e1c b\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m. Ch\u00fang ta kh\u00f4ng ch\u1ec9 c\u1ea7n hi\u1ec3u c\u00f4ng th\u1ee9c v\u00e0 l\u00fd thuy\u1ebft. Nh\u01b0ng c\u0169ng c\u1ea7n m\u1ed9t m\u1eb9o nh\u1ecf \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e2u tr\u1ea3 l\u1eddi m\u1ed9t c\u00e1ch nhanh ch\u00f3ng. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 m\u1eb9o \u0111\u1ec3 gi\u00fap b\u1ea1n nhanh ch\u00f3ng gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m tr\u00ean c\u00f9ng m\u1ed9t ch\u1ee9c n\u0103ng bi\u1ebfn.<\/p>\n<p dir=\"ltr\">V\u00ed d\u1ee5: T\u00ecm ch\u1ee9c n\u0103ng c\u00f9ng m\u1ed9t h\u00e0m tr\u00ean ph\u1ea1m vi r<\/p>\n<p dir=\"ltr\">A. y = (x2+1) 2 \u20263x<\/p>\n<p dir=\"ltr\">B. y = x &#8211; 1\/x<\/p>\n<p dir=\"ltr\">C. y = x<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\">M\u1eb9o 1: \u0110\u01b0\u1ee3c l\u00e0m t\u1eeb tr\u00e1i sang ph\u1ea3i<\/p>\n<p dir=\"ltr\">Ch\u1ecdn c\u00e2u tr\u1ea3 l\u1eddi B. Ch\u00fang t\u00f4i c\u00f3 \u00fd t\u01b0\u1edfng v\u1ec1 m\u1ed9t Y &#039;(0) = -3  0 v\u1edbi t\u1ea5t c\u1ea3 x thu\u1ed9c v\u1ec1 R. V\u00ec v\u1eady, c\u00e2u tr\u1ea3 l\u1eddi B l\u00e0 \u0111\u00fang, v\u00ec v\u1eady ch\u00fang t\u00f4i d\u1eebng l\u1ea1i \u1edf \u0111\u00e2y.<\/p>\n<p dir=\"ltr\">M\u1eb9o 2: S\u1eed d\u1ee5ng th\u1eed nghi\u1ec7m<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110\u1ea7u ti\u00ean, ch\u1ee9c n\u0103ng ho\u1ea1t \u0111\u1ed9ng tr\u00ean R ch\u1eafc ch\u1eafn s\u1ebd ph\u1ea3i \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean R. Do \u0111\u00f3, c\u00e2u tr\u1ea3 l\u1eddi C v\u00e0 D s\u1ebd \u0111\u01b0\u1ee3c lo\u1ea1i tr\u1eeb. <\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">V\u1edbi c\u00e2u tr\u1ea3 l\u1eddi A v\u00ec A l\u00e0 h\u00e0m b\u1ed1n g\u00f3c s\u1ebd c\u00f3 \u0111\u1ea1o h\u00e0m th\u1ee9 ba. H\u01a1n n\u1eefa, \u0111a th\u1ee9c c\u1ee7a l\u1edbp 3 s\u1ebd kh\u00f4ng t\u00edch c\u1ef1c n\u00ean ch\u00fang t\u00f4i lo\u1ea1i b\u1ecf c\u00e2u tr\u1ea3 l\u1eddi A. Do \u0111\u00f3, c\u00e2u tr\u1ea3 l\u1eddi duy nh\u1ea5t B l\u00e0 t\u1ed1t nh\u1ea5t.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Nh\u1eadn x\u00e9t: V\u00ec v\u1eady, \u0111\u1ec3 t\u00ecm c\u00e2u tr\u1ea3 l\u1eddi nhanh nh\u1ea5t cho v\u1ea5n \u0111\u1ec1 tr\u00ean. B\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u1ed9t trong hai m\u1eb9o m\u00e0 kh\u1ec9 g\u1ee3i \u00fd \u1edf tr\u00ean. B\u1eb1ng m\u1ecdi c\u00e1ch, b\u1ea1n v\u1eabn ph\u1ea3i t\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m \u0111\u00f3 \u0111\u1ec3 t\u00ednh to\u00e1n ph\u1ea3n h\u1ed3i nhanh nh\u1ea5t.<\/p>\n<\/li>\n<\/ul>\n<p>Tr\u00ean \u0111\u00e2y l\u00e0 ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 ch\u1ee9c n\u0103ng m\u00e3 h\u00f3a m\u00e0 Kh\u1ec9 mu\u1ed1n g\u1eedi cho t\u1ea5t c\u1ea3 \u0111\u1ed9c gi\u1ea3. V\u1edbi mong mu\u1ed1n truy\u1ec1n b\u00e1 ki\u1ebfn \u200b\u200bth\u1ee9c cho nh\u1eefng ng\u01b0\u1eddi tr\u1ebb tu\u1ed5i \u1edf t\u1ea5t c\u1ea3 c\u00e1c khu v\u1ef1c c\u1ee7a \u0111\u1ea5t n\u01b0\u1edbc. Kh\u1ec9 ch\u00fac b\u1ea1n to\u00e1n t\u1ed1t!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Khi n\u00e0o m\u00e3 c\u1ee7a m\u00e3? \u0110\u00e2y c\u00f3 l\u1ebd l\u00e0 m\u1ed9t c\u00e2u h\u1ecfi khi\u1ebfn nhi\u1ec1u sinh vi\u00ean hoang mang khi g\u1eb7p ph\u1ea3i. \u0110\u1eebng lo l\u1eafng! Trong b\u00e0i vi\u1ebft n\u00e0y, Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef s\u1ebd gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng h\u00f3a to\u00e0n b\u1ed9 ki\u1ebfn \u200b\u200bth\u1ee9c c\u1ee7a Li\u00ean minh. H\u00e3y ch\u00fa \u00fd v\u00e0 \u0111\u1eebng b\u1ecf l\u1ee1&#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-21546","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21546","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=21546"}],"version-history":[{"count":1,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21546\/revisions"}],"predecessor-version":[{"id":25182,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21546\/revisions\/25182"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=21546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=21546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=21546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}