{"id":19729,"date":"2025-07-07T09:35:05","date_gmt":"2025-07-07T02:35:05","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=19729"},"modified":"2025-07-07T09:35:05","modified_gmt":"2025-07-07T02:35:05","slug":"goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/","title":{"rendered":"G\u1ee3i \u00fd b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng \u0111\u1ea1o h\u00e0m trong kinh t\u1ebf v\u00e0 c\u00e1ch h\u1ecdc hi\u1ec7u qu\u1ea3"},"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\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Ung_dung_cua_phai_sinh_trong_kinh_te_la_gi\" >\u1ee8ng d\u1ee5ng c\u1ee7a ph\u00e1i sinh trong kinh t\u1ebf 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\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Cong_thuc_tinh_toan_chuc_nang_trong_nen_kinh_te\" >C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Lam_the_nao_la_chuc_nang_cua_viec_ap_dung_chuc_nang_trong_nen_kinh_te\" >L\u00e0m th\u1ebf n\u00e0o l\u00e0 ch\u1ee9c n\u0103ng c\u1ee7a vi\u1ec7c \u00e1p d\u1ee5ng ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Xu_huong_dao_ham_va_bien_doi_cua_chuc_nang\" >Xu h\u01b0\u1edbng \u0111\u1ea1o h\u00e0m v\u00e0 bi\u1ebfn \u0111\u1ed5i c\u1ee7a ch\u1ee9c n\u0103ng<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Lien_he_voi_dao_ham_va_xu_huong_bien_cua_ham\" >Li\u00ean h\u1ec7 v\u1edbi \u0111\u1ea1o h\u00e0m v\u00e0 xu h\u01b0\u1edbng bi\u1ebfn c\u1ee7a h\u00e0m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Tim_cac_diem_cuc_doan_cua_ham\" >T\u00ecm c\u00e1c \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m<\/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\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Y_nghia_cua_chuc_nang_ap_dung_chuc_nang_trong_kinh_te_hoc\" >\u00dd ngh\u0129a c\u1ee7a ch\u1ee9c n\u0103ng \u00e1p d\u1ee5ng ch\u1ee9c n\u0103ng trong kinh t\u1ebf h\u1ecdc<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Gia_tri_phai_sinh_va_can_bien_trong_nen_kinh_te\" >Gi\u00e1 tr\u1ecb ph\u00e1i sinh v\u00e0 c\u1eadn bi\u00ean trong n\u1ec1n kinh t\u1ebf<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Cap_do_thu_hai_cua_phai_sinh_thu_cap_kem_theo_cac_quy_tac\" >C\u1ea5p \u0111\u1ed9 th\u1ee9 hai c\u1ee7a ph\u00e1i sinh th\u1ee9 c\u1ea5p, k\u00e8m theo c\u00e1c quy t\u1eafc<\/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\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Tinh_toan_he_so_cung_va_cau_do_dan_hoi_theo_gia\" >T\u00ednh to\u00e1n h\u1ec7 s\u1ed1 cung v\u00e0 c\u1ea7u \u0111\u1ed9 \u0111\u00e0n h\u1ed3i theo gi\u00e1<\/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\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Lua_chon_toi_uu_trong_nen_kinh_te\" >L\u1ef1a ch\u1ecdn t\u1ed1i \u01b0u trong n\u1ec1n kinh t\u1ebf<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Chon_muc_dau_ra_toi_uu\" >Ch\u1ecdn m\u1ee9c \u0111\u1ea7u ra t\u1ed1i \u01b0u<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Toi_uu_hoa_toi_uu_dua_tren_cac_yeu_to_dau_vao\" >T\u1ed1i \u01b0u h\u00f3a t\u1ed1i \u01b0u d\u1ef1a tr\u00ean c\u00e1c y\u1ebfu t\u1ed1 \u0111\u1ea7u v\u00e0o<\/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-14\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Danh_sach_cac_bai_tap_ung_dung_chuc_nang_trong_kinh_te_hoc\" >Danh s\u00e1ch c\u00e1c b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng ch\u1ee9c n\u0103ng trong kinh t\u1ebf h\u1ecdc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.ckconitsha.com\/vn\/goi-y-bai-tap-ung-dung-dao-ham-trong-kinh-te-va-cach-hoc-hieu-qua\/#Ket_luan\" >K\u1ebft lu\u1eadn<\/a><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>C\u00e1c b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng kinh t\u1ebf th\u01b0\u1eddng s\u1ebd c\u00f3 r\u1ea5t nhi\u1ec1u ki\u1ebfn \u200b\u200bth\u1ee9c kh\u00f3 kh\u0103n cho sinh vi\u00ean th\u1ef1c h\u00e0nh. Nh\u01b0ng n\u1ebfu h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y b\u1ecb chinh ph\u1ee5c s\u1ebd r\u1ea5t h\u1eefu \u00edch cho t\u01b0\u01a1ng lai c\u1ee7a m\u1ecdi ng\u01b0\u1eddi v\u00ec \u1ee9ng d\u1ee5ng c\u1ee7a h\u1ecd c\u1ef1c k\u1ef3 cao.<\/p>\n<p>                                                                    <img decoding=\"async\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img_default\/monkey3.png\" alt=\"\"><\/p>\n<p class=\"title\">H\u00e0ng tri\u1ec7u tr\u1ebb em \u0111\u00e3 ph\u00e1t tri\u1ec3n c\u00e1c k\u1ef9 n\u0103ng ng\u00f4n ng\u1eef c\u1ee7a ch\u00fang th\u00f4ng qua c\u00e1c \u1ee9ng d\u1ee5ng h\u1ecdc t\u1eadp c\u1ee7a kh\u1ec9<\/p>\n<p class=\"description\">\u0110\u0103ng k\u00fd ngay \u0111\u1ec3 \u0111\u01b0\u1ee3c t\u01b0 v\u1ea5n mi\u1ec5n ph\u00ed v\u1ec1 c\u00e1c s\u1ea3n ph\u1ea9m v\u00e0 tuy\u1ebfn h\u1ecdc h\u1ecdc cho tr\u1ebb em.<\/p>\n<p>                                                                            *Vui l\u00f2ng ki\u1ec3m tra t\u00ean \u0111\u1ea7y \u0111\u1ee7 c\u1ee7a b\u1ea1n *Vui l\u00f2ng ki\u1ec3m tra s\u1ed1 \u0111i\u1ec7n tho\u1ea1i h\u01a1n 2.000 t\u1eeb &amp; 6.000 c\u00e2u ti\u1ebfng Anh \u0111\u1ec3 ph\u00e1t tri\u1ec3n to\u00e0n di\u1ec7n 4 k\u1ef9 n\u0103ng ti\u1ebfng Anh t\u1ed1t &#8211; ti\u1ebfng Anh theo c\u00e1c ph\u01b0\u01a1ng ph\u00e1p hi\u1ec7n \u0111\u1ea1i ph\u00e1t tri\u1ec3n kh\u1ea3 n\u0103ng EQ &amp; Vi\u1ec7t Nam *B\u1ea1n ch\u01b0a ch\u1ecdn b\u1ea5t k\u1ef3 m\u1ee5c n\u00e0o! \u0110\u0103ng k\u00fd t\u01b0 v\u1ea5n mi\u1ec5n ph\u00ed<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Ung_dung_cua_phai_sinh_trong_kinh_te_la_gi\"><\/span>\u1ee8ng d\u1ee5ng c\u1ee7a ph\u00e1i sinh trong kinh t\u1ebf l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">To\u00e1n h\u1ecdc \u0111\u00e3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng r\u1ea5t cao trong kinh t\u1ebf t\u1eeb c\u00f4ng vi\u1ec7c <em>\u0110i th\u1ecb tr\u01b0\u1eddng, mua v\u00e0 b\u00e1n, t\u00ednh to\u00e1n chi ph\u00ed &#8230;<\/em> C\u1ee5 th\u1ec3, v\u1edbi ch\u01b0\u01a1ng ch\u1ee9c n\u0103ng n\u00e0y, ch\u1ee7 y\u1ebfu \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong n\u1ec1n kinh t\u1ebf \u0111\u1ec3 bi\u1ebft t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng kinh t\u1ebf \u0111\u1ec3 \u0111\u01b0a ra quy\u1ebft \u0111\u1ecbnh \u0111\u1ea7u t\u01b0 \u0111\u00fang \u0111\u1eafn.<\/p>\n<p dir=\"ltr\">R\u1ea5t \u0111\u01a1n gi\u1ea3n! \u0110\u1ea7u ti\u00ean, m\u1ecdi ng\u01b0\u1eddi s\u1ebd s\u1eed d\u1ee5ng ch\u1ee9c n\u0103ng m\u00f4 t\u1ea3 s\u1ed1 l\u01b0\u1ee3ng l\u1ee3i \u00edch kinh t\u1ebf, sau \u0111\u00f3 ch\u1ec9 c\u1ea7n \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m \u0111\u1ec3 \u0111\u1ea1o h\u00e0m n\u00f3 c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a doanh nghi\u1ec7p trong t\u01b0\u01a1ng lai.<\/p>\n<p dir=\"ltr\">Ngo\u00e0i ra, trong l\u0129nh v\u1ef1c kinh t\u1ebf, ph\u00e1i sinh c\u0169ng \u00e1p d\u1ee5ng r\u1ea5t nhi\u1ec1u trong vi\u1ec7c d\u1ef1 \u0111o\u00e1n li\u1ec7u ch\u1ee9c n\u0103ng \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t hay l\u1edbn nh\u1ea5t, \u0111\u1ec3 c\u00e1c doanh nghi\u1ec7p c\u00f3 th\u1ec3 t\u1ed1i \u01b0u h\u00f3a c\u00e1c ho\u1ea1t \u0111\u1ed9ng kh\u00e1c nhau m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-1.png\" alt=\"Xu h\u01b0\u1edbng c\u1ee7a c\u00e1c \u1ee9ng d\u1ee5ng to\u00e1n h\u1ecdc trong kinh t\u1ebf l\u00e0 r\u1ea5t nhi\u1ec1u. (\u1ea2nh: Tuoitre)\" width=\"100%\"><\/p>\n<p dir=\"ltr\">C\u1ee5 th\u1ec3, n\u1ebfu h\u00e0m c\u1ee7a h\u00e0m d\u01b0\u01a1ng (h\u00e0m t\u0103ng) v\u00e0 sau \u0111\u00f3 \u0111\u1ed9t nhi\u00ean chuy\u1ec3n sang d\u1eabn xu\u1ea5t nguy\u00ean \u00e2m (h\u00e0m gi\u1ea3m). T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, n\u00f3 \u0111\u00e3 \u0111i qua v\u1ecb tr\u00ed n\u01a1i h\u00e0m \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i \u0111a, c\u0169ng l\u00e0 n\u01a1i m\u00e0 \u0111\u1ea1o h\u00e0m b\u1eb1ng 0.<\/p>\n<p dir=\"ltr\">T\u1eeb nh\u1eadn x\u00e9t n\u00e0y, b\u1eb1ng c\u00e1ch t\u00ecm c\u00e1c v\u1ecb tr\u00ed c\u00f3 \u0111\u1ea1o h\u00e0m, ng\u01b0\u1eddi ta s\u1ebd bi\u1ebft n\u01a1i c\u00f3 m\u1ed9t s\u1ed1 l\u01b0\u1ee3ng s\u1ebd \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t v\u00e0 l\u1edbn nh\u1ea5t, \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a n\u00f3 nh\u01b0 mong mu\u1ed1n.<\/p>\n<p dir=\"ltr\">C\u1ee5 th\u1ec3, d\u1ef1a tr\u00ean \u0111i\u1ec3m n\u00e0y, c\u00f4ng ty s\u1ebd d\u1ec5 d\u00e0ng t\u00ednh to\u00e1n s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m \u0111\u1ec3 s\u1ea3n xu\u1ea5t \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c l\u1ee3i nhu\u1eadn t\u1ed1t nh\u1ea5t.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cong_thuc_tinh_toan_chuc_nang_trong_nen_kinh_te\"><\/span>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u1ee9c n\u0103ng l\u1ee3i nhu\u1eadn c\u1ee7a nh\u00e0 s\u1ea3n xu\u1ea5t nh\u01b0 sau: <\/p>\n<p dir=\"ltr\" style=\"text-align: center\">P = &#8211; 1\/3Q3 + 14Q2 + 60Q &#8211; 54<\/p>\n<p dir=\"ltr\">Trong \u0111\u00f3:<\/p>\n<ul>\n<li dir=\"ltr\">P l\u00e0 l\u1ee3i nhu\u1eadn c\u1ee7a nh\u00e0 s\u1ea3n xu\u1ea5t<\/li>\n<li dir=\"ltr\">Q l\u00e0 m\u1ee9c \u0111\u1ea7u ra cho l\u1ee3i nhu\u1eadn p<\/li>\n<\/ul>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Lam_the_nao_la_chuc_nang_cua_viec_ap_dung_chuc_nang_trong_nen_kinh_te\"><\/span>L\u00e0m th\u1ebf n\u00e0o l\u00e0 ch\u1ee9c n\u0103ng c\u1ee7a vi\u1ec7c \u00e1p d\u1ee5ng ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Trong kinh t\u1ebf, to\u00e1n h\u1ecdc c\u00f3 m\u1ed9t \u00fd ngh\u0129a l\u1edbn \u0111\u1ec3 gi\u00fap c\u00e1c doanh nghi\u1ec7p t\u00ednh to\u00e1n k\u1ebft qu\u1ea3 v\u00e0 m\u1ee5c ti\u00eau h\u1ecd \u0111\u1eb7t ra. C\u1ee5 th\u1ec3, v\u1edbi chuy\u00ean m\u00f4n to\u00e1n to\u00e1n, ch\u00fang th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong kinh t\u1ebf v\u1edbi c\u00e1c lo\u1ea1i b\u00e0i t\u1eadp c\u01a1 b\u1ea3n nh\u01b0:<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Xu_huong_dao_ham_va_bien_doi_cua_chuc_nang\"><\/span>Xu h\u01b0\u1edbng \u0111\u1ea1o h\u00e0m v\u00e0 bi\u1ebfn \u0111\u1ed5i c\u1ee7a ch\u1ee9c n\u0103ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Trong d\u1ea1ng n\u00e0y c\u1ee7a h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc to\u00e1n h\u1ecdc, hai v\u1ea5n \u0111\u1ec1 l\u00e0 m\u1ed1i quan h\u1ec7 gi\u1eefa \u0111\u1ea1o h\u00e0m v\u00e0 xu h\u01b0\u1edbng bi\u1ebfn \u0111\u1ed5i c\u1ee7a h\u00e0m, c\u00f9ng v\u1edbi vi\u1ec7c x\u00e1c \u0111\u1ecbnh ch\u1ee9c n\u0103ng t\u0103ng v\u00e0 gi\u1ea3m ch\u1ee9c n\u0103ng. c\u1ee5 th\u1ec3:<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-2.png\" alt=\"D\u1ef1a tr\u00ean xu h\u01b0\u1edbng bi\u1ebfn c\u1ee7a h\u00e0m \u0111\u1ec3 t\u00ednh to\u00e1n. (\u1ea2nh; B\u00e1o Tuoitre)\" width=\"100%\"><\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Lien_he_voi_dao_ham_va_xu_huong_bien_cua_ham\"><\/span>Li\u00ean h\u1ec7 v\u1edbi \u0111\u1ea1o h\u00e0m v\u00e0 xu h\u01b0\u1edbng bi\u1ebfn c\u1ee7a h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\"><em>\u0110\u1ecbnh l\u00fd 1: \u0110i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft<\/em><\/p>\n<p dir=\"ltr\">N\u1ebfu h\u00e0m f (x) c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i b\u1ea5t k\u1ef3 \u0111i\u1ec3m n\u00e0o c\u1ee7a kho\u1ea3ng (a; b) th\u00ec:<\/p>\n<ul>\n<li class=\"MsoNormal\">f (x) \u0111\u01a1n \u0111i\u1ec7u t\u0103ng tr\u00ean ph\u1ea1m vi (a; b) =&gt; f &#039;(x) 0, &#8220;x\u00ee (a; b)<\/li>\n<li class=\"MsoNormal\">f (x) \u0111\u01a1n \u0111i\u1ec7u gi\u1ea3m tr\u00ean ph\u1ea1m vi (a; b) =&gt; f &#039;(x) \u00a3 0, &#8220;x\u00ee (a; b)<\/li>\n<\/ul>\n<p dir=\"ltr\"><em>\u0110\u1ecbnh l\u00fd 2: \u0110i\u1ec1u ki\u1ec7n \u0111\u1ee7<\/em><\/p>\n<p dir=\"ltr\">N\u1ebfu h\u00e0m f (x) c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i b\u1ea5t k\u1ef3 \u0111i\u1ec3m n\u00e0o c\u1ee7a kho\u1ea3ng (a; b) th\u00ec:<\/p>\n<ul>\n<li class=\"MsoNormal\">f &#039;(x)&gt; 0, &#8220;x\u00ee (a; b) =&gt; f (x) \u0111\u01a1n \u0111i\u1ec7u t\u0103ng tr\u00ean ph\u1ea1m vi (a; b)<\/li>\n<li class=\"MsoNormal\">f &#039;(x)  f (x) \u0111\u01a1n \u0111i\u1ec7u gi\u1ea3m trong kho\u1ea3ng th\u1eddi gian (a; b)<\/li>\n<li>f &#039;(x) = 0, &#8220;x\u00ee (a; b) =&gt; f (x) c\u00f3 gi\u00e1 tr\u1ecb kh\u00f4ng \u0111\u1ed5i tr\u00ean kho\u1ea3ng (a; b)<\/li>\n<\/ul>\n<p><em>X\u00e1c \u0111\u1ecbnh s\u1ef1 gia t\u0103ng v\u00e0 gi\u1ea3m ch\u1ee9c n\u0103ng<\/em><\/p>\n<p dir=\"ltr\">\u0110\u1ec3 c\u00f3 th\u1ec3 t\u00ednh to\u00e1n s\u1ef1 gia t\u0103ng v\u00e0 gi\u1ea3m m\u1ed9 c\u1ee7a h\u00e0m y = f (x) trong n\u1ec1n kinh t\u1ebf, m\u1ecdi ng\u01b0\u1eddi d\u1ef1a v\u00e0o c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li dir=\"ltr\">B\u01b0\u1edbc 1: X\u00e1c \u0111\u1ecbnh mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 2: T\u00ednh ch\u1ee9c n\u0103ng t\u01b0\u01a1ng \u1ee9ng c\u1ee7a h\u00e0m<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 3: Ti\u1ebfn h\u00e0nh xem x\u00e9t d\u1ea5u hi\u1ec7u c\u1ee7a h\u00e0m v\u1eeba \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n.<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 4: T\u1eeb b\u1ea3ng con d\u1ea5u ph\u00e1i sinh, ti\u1ebfn h\u00e0nh k\u1ebft th\u00fac s\u1ef1 gia t\u0103ng ho\u1eb7c gi\u1ea3m ch\u1ee9c n\u0103ng t\u01b0\u01a1ng \u1ee9ng.<\/li>\n<\/ul>\n<p dir=\"ltr\">V\u00ed d\u1ee5:<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-3a.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Tim_cac_diem_cuc_doan_cua_ham\"><\/span>T\u00ecm c\u00e1c \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a h\u00e0m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ecbnh ngh\u0129a: Cho h\u00e0m f (x) \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh li\u00ean t\u1ee5c tr\u00ean kho\u1ea3ng (a; b). Trong \u0111\u00f3:<\/p>\n<ul>\n<li class=\"MsoNormal\">f (x) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1ed1i \u0111a t\u1ea1i \u0111i\u1ec3m x0 (a; b) n\u1ebfu $ d&gt; 0 sao cho: &#8220;x\u00ee (a; b), 0 &lt;| x &#8211; x0 | x &#8211; &lt;| x &#8211; x0 |<\/li>\n<li class=\"MsoNormal\">f (x) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1ed1i thi\u1ec3u t\u1ea1i \u0111i\u1ec3m x0 \u00ee (a; b) n\u1ebfu $ d&gt; 0 sao cho: &#8220;x\u00ee (a; b), 0 &lt;| x &#8211; x0 | x &#8211; x0 |  f (x0) f (x0)<\/li>\n<\/ul>\n<p dir=\"ltr\">C\u1ee5 th\u1ec3, \u0111i\u1ec3m t\u1ed1i thi\u1ec3u v\u00e0 t\u1ed1i \u0111a s\u1ebd \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a m\u1ed9t h\u00e0m.<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-4a.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<p dir=\"ltr\">Do \u0111\u00f3, \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y \u0111i\u1ec3m c\u1ef1c \u0111oan c\u1ee7a ch\u1ee9c n\u0103ng trong ch\u1ee9c n\u0103ng \u00e1p d\u1ee5ng ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf, \u0111\u00f2i h\u1ecfi ph\u1ea3i n\u1eafm b\u1eaft c\u00e1c \u0111i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft v\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 c\u1ee7a ch\u00fang. C\u1ee5 th\u1ec3:<\/p>\n<p dir=\"ltr\"><em>\u0110i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft:<\/em><\/p>\n<p class=\"MsoNormal\">N\u1ebfu h\u00e0m f (x) \u0111\u1ea1t c\u1ef1c \u0111\u1ed9 t\u1ea1i x0\u00ee (a; b) v\u00e0 f (x) c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i x0 th\u00ec: f &#039;(x0) = 0<\/p>\n<p dir=\"ltr\">K\u1ebft lu\u1eadn: H\u00e0m f (x) \u0111\u01b0\u1ee3c \u0111\u01b0a ra ch\u1ec9 c\u00f3 th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb t\u1ed1i \u0111a \u1edf gi\u1edbi h\u1ea1n t\u01b0\u01a1ng \u1ee9ng c\u1ee7a -, ch\u00fang thu\u1ed9c v\u1ec1 m\u1ed9t trong hai lo\u1ea1i l\u00e0 \u0111i\u1ec3m d\u1eebng (\u0111i\u1ec3m m\u00e0 \u0111\u1ea1o h\u00e0m t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3 \u0111\u01b0\u1ee3c lo\u1ea1i b\u1ecf) v\u00e0 \u0111i\u1ec3m m\u00e0 h\u00e0m li\u00ean t\u1ee5c nh\u01b0ng kh\u00f4ng c\u00f3 \u0111\u1ea1o h\u00e0m.<\/p>\n<p dir=\"ltr\"><em>\u0110i\u1ec1u ki\u1ec7n \u0111\u1ee7:<\/em><\/p>\n<p class=\"MsoNormal\">Gi\u1ea3 s\u1eed X0 l\u00e0 m\u1ed9t trong nh\u1eefng \u0111i\u1ec3m quan tr\u1ecdng c\u1ee7a h\u00e0m v\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a ch\u00fang c\u00f3 d\u1ea5u tr\u00ean kho\u1ea3ng (x0 &#8211; d; x0), (x0; x0+ d) c\u1ee7a x0.<\/p>\n<p class=\"MsoNormal\">N\u1ebfu ch\u00fang \u0111i qua \u0111i\u1ec3m x0 v\u1edbi \u0111\u1ea1o h\u00e0m t\u01b0\u01a1ng \u1ee9ng, ch\u1ee9c n\u0103ng s\u1ebd \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3<\/p>\n<ul>\n<li class=\"MsoNormal\">X0 l\u00e0 \u0111i\u1ec3m t\u1ed1i \u0111a n\u1ebfu f &#039;(x) thay \u0111\u1ed5i t\u1eeb + th\u00e0nh &#8211; th\u00e0nh;<\/li>\n<li class=\"MsoNormal\">X0 l\u00e0 \u0111i\u1ec3m t\u1ed1i thi\u1ec3u n\u1ebfu f &#039;(x) thay \u0111\u1ed5i d\u1ea5u t\u1eeb &#8211; th\u00e0nh +;<\/li>\n<li dir=\"ltr\">N\u1ebfu vi\u1ec7c v\u01b0\u1ee3t qua \u0111i\u1ec3m X0 v\u00e0 \u200b\u200b\u0111\u1ea1o h\u00e0m kh\u00f4ng thay \u0111\u1ed5i d\u1ea5u hi\u1ec7u, h\u00e0m s\u1ebd kh\u00f4ng \u0111\u1ea1t \u0111\u1ebfn c\u1ef1c \u0111i\u1ec3m t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3.<\/li>\n<\/ul>\n<p dir=\"ltr\"><em>T\u00ecm ki\u1ebfm c\u00e1c b\u01b0\u1edbc c\u1ee7a m\u1ed9t ch\u1ee9c n\u0103ng<\/em><\/p>\n<p dir=\"ltr\">\u0110\u1ec3 c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y c\u1ef1c \u0111oan c\u1ee7a h\u00e0m y = f (x) tr\u01b0\u1edbc, b\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li dir=\"ltr\">B\u01b0\u1edbc 1: T\u00ednh to\u00e1n mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m t\u01b0\u01a1ng \u1ee9ng<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 2: T\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 3: T\u00ednh \u0111i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft c\u1ee7a ch\u1ee9c n\u0103ng \u0111\u1ec3 t\u00ecm m\u1ed9t \u0111i\u1ec3m quan tr\u1ecdng. Bao g\u1ed3m t\u00ecm th\u1ea5y c\u00e1c \u0111i\u1ec3m d\u1eebng ho\u1eb7c ch\u1ec9 ra c\u00e1c \u0111i\u1ec3m trong mi\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u1edf \u0111\u00f3, h\u00e0m l\u00e0 li\u00ean t\u1ee5c nh\u01b0ng kh\u00f4ng c\u00f3 \u0111\u1ea1o h\u00e0m.<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 4: Xem x\u00e9t c\u00e1c \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 c\u1ee7a \u0111\u1ea1o h\u00e0m v\u1edbi t\u1eebng \u0111i\u1ec3m quan tr\u1ecdng v\u00e0 k\u1ebft lu\u1eadn t\u01b0\u01a1ng \u1ee9ng.<\/li>\n<\/ul>\n<p dir=\"ltr\">V\u00ed d\u1ee5:<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-5a.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Y_nghia_cua_chuc_nang_ap_dung_chuc_nang_trong_kinh_te_hoc\"><\/span>\u00dd ngh\u0129a c\u1ee7a ch\u1ee9c n\u0103ng \u00e1p d\u1ee5ng ch\u1ee9c n\u0103ng trong kinh t\u1ebf h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">V\u1ec1 vi\u1ec7c x\u00e1c \u0111\u1ecbnh \u00fd ngh\u0129a c\u1ee7a ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf s\u1ebd ti\u1ebfn h\u00e0nh t\u00ednh to\u00e1n gi\u00e1 tr\u1ecb ph\u00e1i sinh v\u00e0 gi\u00e1 tr\u1ecb c\u1eadn bi\u00ean trong n\u1ec1n kinh t\u1ebf, c\u0169ng nh\u01b0 d\u1eabn xu\u1ea5t th\u1ee9 hai v\u1edbi quy t\u1eafc l\u1ee3i \u00edch c\u1ea1nh. C\u1ee5 th\u1ec3<\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Gia_tri_phai_sinh_va_can_bien_trong_nen_kinh_te\"><\/span>Gi\u00e1 tr\u1ecb ph\u00e1i sinh v\u00e0 c\u1eadn bi\u00ean trong n\u1ec1n kinh t\u1ebf<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">\u1ede \u0111\u00e2y s\u1ebd ti\u1ebfn h\u00e0nh gi\u00e1 tr\u1ecb ph\u00e1i sinh v\u00e0 bi\u00ean gi\u1edbi c\u1ea5p 1. C\u1ee5 th\u1ec3, khi xem x\u00e9t m\u00f4 h\u00ecnh h\u00e0m y = f (x), trong \u0111\u00f3 x v\u00e0 y l\u00e0 c\u00e1c bi\u1ebfn kinh t\u1ebf.<\/p>\n<p class=\"MsoNormal\">T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, gi\u00e1 tr\u1ecb c\u1ee7a y &#8211; \u0111\u01b0\u1eddng vi\u1ec1n c\u1ee7a x t\u1ea1i x = x0 (mf (x0)) l\u00e0 gi\u00e1 tr\u1ecb m\u00f4 t\u1ea3 s\u1ef1 thay \u0111\u1ed5i gi\u00e1 tr\u1ecb c\u1ee7a y khi x bi\u1ebfn \u0111\u1ed5i 1 \u0111\u01a1n v\u1ecb \u1edf gi\u00e1 tr\u1ecb ban \u0111\u1ea7u x = x0, t\u01b0\u01a1ng \u1ee9ng v\u1edbi mf (x0) = f (x0+1) &#8211; f (x0).<\/p>\n<p dir=\"ltr\">Khi li\u00ean h\u1ec7 v\u1edbi \u0111\u1ea1o h\u00e0m, ch\u00fang ta c\u00f3: mf (x0) = f (x0+1) &#8211; f (x0) f &#039;(x0).<\/p>\n<p dir=\"ltr\">M\u1ed9t s\u1ed1 m\u00f4 h\u00ecnh h\u00e0m c\u1eadn bi\u00ean nh\u01b0:<\/p>\n<ul>\n<li dir=\"ltr\">H\u00e0m chi ph\u00ed s\u1ea3n xu\u1ea5t: TC = TC (Q)<\/li>\n<li dir=\"ltr\">Chi ph\u00ed: MC = TC &#039;(Q)<\/li>\n<li dir=\"ltr\">H\u00e0m doanh thu: tr = tr (q)<\/li>\n<li dir=\"ltr\">Doanh thu bi\u00ean gi\u1edbi: MR = TR &#039;(Q)<\/li>\n<li dir=\"ltr\">H\u00e0m benade: u = u (x)<\/li>\n<li dir=\"ltr\">L\u1ee3i \u00edch: Mu = u &#039;(x)<\/li>\n<li dir=\"ltr\">Ch\u1ee9c n\u0103ng s\u1ea3n xu\u1ea5t ng\u1eafn h\u1ea1n: q = f (l)<\/li>\n<li dir=\"ltr\">Gi\u00e1 tr\u1ecb c\u1ee7a s\u1ea3n ph\u1ea9m t\u1ea1o t\u00e1c ranh gi\u1edbi c\u1ee7a lao \u0111\u1ed9ng: mppl = f &#039;(l).<\/li>\n<\/ul>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/bai-tap-ung-dung-dao-ham-trong-kinh-te-6.png\" alt=\"(Ngu\u1ed3n: T\u00f3m t\u1eaft)\" width=\"100%\"><\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cap_do_thu_hai_cua_phai_sinh_thu_cap_kem_theo_cac_quy_tac\"><\/span>C\u1ea5p \u0111\u1ed9 th\u1ee9 hai c\u1ee7a ph\u00e1i sinh th\u1ee9 c\u1ea5p, k\u00e8m theo c\u00e1c quy t\u1eafc<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">D\u1ef1a tr\u00ean m\u00f4 h\u00ecnh h\u00e0m y = f (x), trong \u0111\u00f3 y l\u00e0 bi\u1ebfn l\u1ee3i \u00edch c\u1ee7a doanh nghi\u1ec7p (nh\u01b0 l\u1ee3i nhu\u1eadn, doanh thu, thu nh\u1eadp &#8230;) v\u00e0 x l\u00e0 m\u00f4 t\u1ea3 bi\u1ebfn c\u1ee7a y\u1ebfu t\u1ed1 mang l\u1ea1i gi\u00e1 tr\u1ecb Y.<\/p>\n<p dir=\"ltr\">Quy t\u1eafc c\u1ee7a l\u1ee3i \u00edch c\u1ea1nh s\u1ebd gi\u1ea3m d\u1ea7n n\u00f3i r\u1eb1ng X c\u00e0ng l\u1edbn, ranh gi\u1edbi c\u00e0ng nh\u1ecf. \u0110\u1ed3ng th\u1eddi, \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 t\u00f4i gi\u1ea3m \u00fb f (x) \u00a3 0.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Tinh_toan_he_so_cung_va_cau_do_dan_hoi_theo_gia\"><\/span>T\u00ednh to\u00e1n h\u1ec7 s\u1ed1 cung v\u00e0 c\u1ea7u \u0111\u1ed9 \u0111\u00e0n h\u1ed3i theo gi\u00e1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Vi\u1ec7c t\u00ednh to\u00e1n h\u1ec7 s\u1ed1 \u0111\u1ed9 co gi\u00e3n c\u1ee7a nhu c\u1ea7u \u1edf m\u1ee9c gi\u00e1 ch\u00ednh l\u00e0 t\u00ednh to\u00e1n do s\u1ed1 l\u01b0\u1ee3ng thay \u0111\u1ed5i d\u1ef1a tr\u00ean % s\u1ed1 l\u01b0\u1ee3ng nhu c\u1ea7u khi gi\u00e1 t\u0103ng 1 %.<\/p>\n<p class=\"MsoNormal\">\u1ede \u0111\u00e2y, ch\u00fang ta c\u00f3 h\u00e0m c\u1ea7u qd \u200b\u200b= d (p), t\u01b0\u01a1ng \u1ee9ng. ed = d &#039;(p). P\/D (P)<\/p>\n<p dir=\"ltr\">V\u00e0 h\u1ec7 s\u1ed1 \u0111\u1ed9 co gi\u00e3n c\u1ee7a ngu\u1ed3n cung \u1edf gi\u00e1 ch\u00ednh l\u00e0 t\u00ednh to\u00e1n thay \u0111\u1ed5i \u0111o l\u01b0\u1eddng d\u1ef1a tr\u00ean % ngu\u1ed3n cung khi gi\u00e1 t\u0103ng 1 %.<\/p>\n<p class=\"MsoNormal\">\u1ede \u0111\u00e2y, ch\u00fang ta c\u00f3 ARC QS = S (P), t\u01b0\u01a1ng \u1ee9ng. Es = s &#039;(p). P\/S (P)<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-7.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Lua_chon_toi_uu_trong_nen_kinh_te\"><\/span>L\u1ef1a ch\u1ecdn t\u1ed1i \u01b0u trong n\u1ec1n kinh t\u1ebf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">T\u00f9y ch\u1ecdn t\u1ed1i \u01b0u trong n\u1ec1n kinh t\u1ebf d\u1ef1a tr\u00ean \u0111\u1ea1o h\u00e0m s\u1ebd ti\u1ebfn h\u00e0nh ch\u1ecdn m\u1ee9c \u0111\u1ea7u ra t\u1ed1i \u01b0u c\u00f9ng v\u1edbi vi\u1ec7c s\u1eed d\u1ee5ng t\u1ed1i \u01b0u t\u1ed1i \u01b0u d\u1ef1a tr\u00ean y\u1ebfu t\u1ed1 \u0111\u1ea7u v\u00e0o. C\u1ee5 th\u1ec3:<\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Chon_muc_dau_ra_toi_uu\"><\/span>Ch\u1ecdn m\u1ee9c \u0111\u1ea7u ra t\u1ed1i \u01b0u<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li dir=\"ltr\">T\u1ed5ng chi ph\u00ed: TC = TC (Q)<\/li>\n<li dir=\"ltr\">T\u1ed5ng doanh thu: tr = tr (q).<\/li>\n<\/ul>\n<p dir=\"ltr\">Y\u00eau c\u1ea7u c\u1ea7n ch\u1ecdn \u0111\u1ea7u ra Q \u0111\u1ec3 l\u1ee3i nhu\u1eadn t\u1ed1i \u0111a?<\/p>\n<p dir=\"ltr\">Gi\u1ea3i ph\u00e1p:<\/p>\n<p class=\"MsoNormal\">T\u00ecm q sao cho p = tr (q) &#8211; tc (q) \u0111\u1ea1t gi\u00e1 tr\u1ecb t\u1ed1i \u0111a. \u0110i\u1ec1u ki\u1ec7n c\u1ea7n thi\u1ebft l\u00e0 p &#039;= tr&#039; (q) &#8211; tc &#039;(q) = 0 \u00fb mr = mc.<\/p>\n<p class=\"MsoNormal\">T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, l\u1ee3i nhu\u1eadn s\u1ebd \u0111\u1ea1t t\u1ed1i \u0111a n\u1ebfu doanh thu c\u1eadn bi\u00ean c\u1ee7a c\u00f4ng ty s\u1ebd ph\u1ea3i b\u1eb1ng v\u1edbi chi ph\u00ed. T\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111i\u1ec1u ki\u1ec7n ch\u00ednh l\u00e0: P &#8221; &lt;0 \u00fb tr &#039;&#039; (q)<\/p>\n<p class=\"MsoNormal\">L\u01b0u \u00fd: Khi th\u1ef1c hi\u1ec7n t\u00ednh to\u00e1n n\u00e0y, m\u1ecdi ng\u01b0\u1eddi c\u1ea7n ki\u1ec3m tra c\u00e1c \u0111i\u1ec1u ki\u1ec7n ch\u00ednh x\u00e1c d\u1ef1a tr\u00ean d\u1ea5u hi\u1ec7u h\u00e0m c\u1ea5p 1.<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-8.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<h4 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Toi_uu_hoa_toi_uu_dua_tren_cac_yeu_to_dau_vao\"><\/span>T\u1ed1i \u01b0u h\u00f3a t\u1ed1i \u01b0u d\u1ef1a tr\u00ean c\u00e1c y\u1ebfu t\u1ed1 \u0111\u1ea7u v\u00e0o<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p dir=\"ltr\">\u1ede \u0111\u00e2y m\u1ecdi ng\u01b0\u1eddi s\u1ebd s\u1eed d\u1ee5ng:<\/p>\n<ul>\n<li dir=\"ltr\">Ch\u1ee9c n\u0103ng s\u1ea3n xu\u1ea5t ng\u1eafn h\u1ea1n t\u01b0\u01a1ng \u1ee9ng l\u00e0 q = f (l)<\/li>\n<li dir=\"ltr\">Gi\u00e1 s\u1ea3n ph\u1ea9m l\u00e0 P; Gi\u00e1 lao \u0111\u1ed9ng l\u00e0 WL; Chi ph\u00ed c\u1ed1 \u0111\u1ecbnh l\u00e0 C0<\/li>\n<\/ul>\n<p dir=\"ltr\">T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, ch\u1ecdn m\u1ee9c \u0111\u1ed9 vi\u1ec7c l\u00e0m \u0111\u1ec3 ti\u1ebft ki\u1ec7m chi ph\u00ed, \u0111\u1ea1t l\u1ee3i nhu\u1eadn t\u1ed1i \u0111a?<\/p>\n<p dir=\"ltr\">Gi\u1ea3i ph\u00e1p: \u0110\u1ea7u ti\u00ean, b\u1ea1n c\u1ea7n t\u00ecm L sao cho p = pf (l) &#8211; wl.l &#8211; c0 \u0111\u1ea1t \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb t\u1ed1i \u0111a.<\/p>\n<p class=\"MsoNormal\">\u0110i\u1ec1u ki\u1ec7n t\u01b0\u01a1ng \u1ee9ng l\u00e0 p &#039;= 0 \u00fb p.mppl &#8211; wl = 0. T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, l\u1ee3i nhu\u1eadn s\u1ebd \u0111\u1ea1t \u0111\u1ebfn m\u1ee9c t\u1ed1i \u0111a n\u1ebfu gi\u00e1 tr\u1ecb c\u1ee7a ti\u1ec1n c\u1ee7a s\u1ea3n ph\u1ea9m t\u1ea1o t\u00e1c hi\u1ec7n t\u1ea1i c\u1ee7a lao \u0111\u1ed9ng s\u1ebd b\u1eb1ng v\u1edbi ti\u1ec1n thu\u00ea lao \u0111\u1ed9ng.<\/p>\n<p class=\"MsoNormal\">\u0110i\u1ec1u ki\u1ec7n \u0111\u1ee7 l\u00e0 khi P &#8221; &lt;0 \u00fb f &quot;(l) &lt;0. T\u01b0\u01a1ng t\u1ef1, \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c xem x\u00e9t d\u1ef1a tr\u00ean c\u00e1c d\u1ea5u hi\u1ec7u c\u1ee7a \u0111\u1ea1o h\u00e0m c\u1ea5p 1.<\/p>\n<p class=\"MsoNormal\">\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/bai-tap-ung-dung-dao-ham-trong-kinh-te-9.png\" alt=\"(Ngu\u1ed3n: Edutop)\" width=\"100%\"><\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Danh_sach_cac_bai_tap_ung_dung_chuc_nang_trong_kinh_te_hoc\"><\/span>Danh s\u00e1ch c\u00e1c b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng ch\u1ee9c n\u0103ng trong kinh t\u1ebf h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">D\u1ef1a tr\u00ean ki\u1ebfn \u200b\u200bth\u1ee9c l\u00fd thuy\u1ebft \u1edf tr\u00ean, \u0111\u1ec3 th\u1ea5y t\u1ea7m quan tr\u1ecdng c\u1ee7a ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf, \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u0111\u1ec3 h\u1ecd \u00e1p d\u1ee5ng v\u00e0 th\u1ef1c h\u00e0nh.<\/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\/bai-tap-ung-dung-dao-ham-trong-kinh-te-10.png\" alt=\"(Ngu\u1ed3n: T\u00f3m t\u1eaft)\" width=\"100%\"><\/p>\n<p>Xem th\u00eam: C\u00f4ng th\u1ee9c ch\u1ee9c n\u0103ng n\u00e2ng cao 11 v\u00e0 c\u00e1c k\u1ef9 n\u0103ng tuy\u1ec7t v\u1eddi \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i t\u1eadp t\u1ed1t nh\u1ea5t c\u1ee7a h\u1ecdc sinh n\u00ean bi\u1ebft<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Ket_luan\"><\/span>K\u1ebft lu\u1eadn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t b\u1ea3n t\u00f3m t\u1eaft v\u1ec1 th\u00f4ng tin \u0111\u01b0\u1ee3c cung c\u1ea5p v\u1ec1 \u00fd ngh\u0129a v\u00e0 t\u1ea7m quan tr\u1ecdng c\u1ee7a c\u00e1c b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng ch\u1ee9c n\u0103ng trong n\u1ec1n kinh t\u1ebf. Do \u0111\u00f3, c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng to\u00e1n h\u1ecdc l\u00e0 m\u1ed9t ch\u1ee7 \u0111\u1ec1 quan tr\u1ecdng, mang l\u1ea1i nhi\u1ec1u gi\u00e1 tr\u1ecb h\u01a1n \u0111\u1ec3 h\u1ed7 tr\u1ee3 c\u00f4ng vi\u1ec7c kinh t\u1ebf t\u1ed1t h\u01a1n.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00e1c b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng kinh t\u1ebf th\u01b0\u1eddng s\u1ebd c\u00f3 r\u1ea5t nhi\u1ec1u ki\u1ebfn \u200b\u200bth\u1ee9c kh\u00f3 kh\u0103n cho sinh vi\u00ean th\u1ef1c h\u00e0nh. Nh\u01b0ng n\u1ebfu h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y b\u1ecb chinh ph\u1ee5c s\u1ebd r\u1ea5t h\u1eefu \u00edch cho t\u01b0\u01a1ng lai c\u1ee7a m\u1ecdi ng\u01b0\u1eddi v\u00ec \u1ee9ng d\u1ee5ng c\u1ee7a h\u1ecd c\u1ef1c k\u1ef3 cao. H\u00e0ng tri\u1ec7u tr\u1ebb em \u0111\u00e3 ph\u00e1t&#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-19729","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/19729","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=19729"}],"version-history":[{"count":1,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/19729\/revisions"}],"predecessor-version":[{"id":24416,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/19729\/revisions\/24416"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=19729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=19729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=19729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}