{"id":772,"date":"2026-05-05T05:04:07","date_gmt":"2026-05-05T05:04:07","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-cau-hoi-ham-so-phat-trien-tu-de-thi-thptqg-anh-giao-kid\/"},"modified":"2026-05-05T07:39:01","modified_gmt":"2026-05-05T07:39:01","slug":"bo-cau-hoi-ham-so-phat-trien-tu-de-thi-thptqg-anh-giao-kid","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-cau-hoi-ham-so-phat-trien-tu-de-thi-thptqg-anh-giao-kid\/","title":{"rendered":"B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid"},"content":{"rendered":"

B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/strong> c\u00f3 c\u1ea5u tr\u00fac v\u00e0 d\u1ea1ng b\u00e0i c\u1ee7a \u0111\u1ec1 thi THPTQG ch\u00ednh th\u1ee9c. T\u00e0i li\u1ec7u t\u1eadp trung v\u00e0o chuy\u00ean \u0111\u1ec1 H\u00e0m S\u1ed1 v\u1edbi c\u00e1c c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i r\u00f5 r\u00e0ng, t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao. Ngo\u00e0i ra, b\u1ed9 c\u00e2u h\u1ecfi g\u1ed3m c\u00e1c v\u00ed d\u1ee5 minh h\u1ecda c\u1ee5 th\u1ec3 v\u00e0 h\u01b0\u1edbng d\u1eabn chi ti\u1ebft gi\u00fap h\u1ecdc sinh c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n kh\u00f3. H\u00f4m nay, Tailieuonthi Edu<\/strong><\/a> s\u1ebd gi\u00fap c\u00e1c b\u1ea1n kh\u00e1m ph\u00e1 to\u00e0n b\u1ed9 c\u00e1c c\u00e2u h\u1ecfi n\u00e0y \u0111\u1ec3 t\u1ef1 tin chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao trong k\u1ef3 thi s\u1eafp t\u1edbi.<\/p>\n

N\u1ed9i dung B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/strong><\/h2>\n

B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/strong> g\u1ed3m b\u1ed9 c\u00e2u h\u1ecfi v\u1ec1 h\u00e0m s\u1ed1, \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG 2025 c\u1ee7a Anh Gi\u00e1o Kid. T\u00e0i li\u1ec7u to\u00e1n 12<\/strong><\/a> n\u00e0y \u0111\u01b0\u1ee3c chia th\u00e0nh 3 ph\u1ea7n ch\u00ednh, m\u1ed7i ph\u1ea7n t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t d\u1ea1ng b\u00e0i \u0111i\u1ec3n h\u00ecnh trong \u0111\u1ec1 thi:<\/p>\n

C\u00c2U 1: Ti\u1ec7m c\u1eadn v\u00e0 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/strong><\/p>\n

V\u00ed d\u1ee5 1:<\/strong> Cho h\u00e0m s\u1ed1 $y = f(x)$ c\u00f3 $\\lim_{x \\to +\\infty} f(x) = 3$ v\u00e0 $\\lim_{x \\to -\\infty} f(x) = -3$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang?<\/p>\n

A. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai ti\u1ec7m c\u1eadn ngang l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $x = 3$ v\u00e0 $x = -3$.
\nB. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn ngang.
\nC. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u00fang m\u1ed9t ti\u1ec7m c\u1eadn ngang.
\nD. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $y = 3$ v\u00e0 $y = -3$.<\/p>\n

V\u00ed d\u1ee5 2:<\/strong> \u0110\u01b0\u1eddng th\u1eb3ng $y = ax \u2013 b$ l\u00e0 ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y = f(x)$. M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/p>\n

A. $\\lim_{x \\to +\\infty} (f(x) \u2013 ax + b) = a$.
\nB. $\\lim_{x \\to +\\infty} (f(x) \u2013 ax + b) = 0$ ho\u1eb7c $\\lim_{x \\to -\\infty} (f(x) \u2013 ax + b) = 0$.
\nC. $\\lim_{x \\to +\\infty} (f(x) \u2013 ax + b) = b$.
\nD. $\\lim_{x \\to +\\infty} (f'(x) \u2013 ax + b) = 0$.<\/p>\n

C\u00c2U 2: \u0110\u1ea1o h\u00e0m, C\u1ef1c tr\u1ecb, Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u2013 nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1<\/strong><\/p>\n

V\u00ed d\u1ee5 1:<\/strong> Cho h\u00e0m s\u1ed1 $f(x) = -x^3 + 3x^2 + 3$.<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u1ea1o h\u00e0m l\u00e0 $f'(x) = -3x^2 \u2013 6x$.
\nb) Ph\u01b0\u01a1ng tr\u00ecnh $f'(x)=0$ c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t.
\nc) $f(2)=7$.
\nd) T\u1ed5ng gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t v\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 $f(x)$ tr\u00ean \u0111o\u1ea1n $[-3;3]$ b\u1eb1ng 60.<\/p>\n

V\u00ed d\u1ee5 2:<\/strong> Cho h\u00e0m s\u1ed1 $f(x) = -2x^4 + 4x^2 + 1$ c\u00f3 \u0111\u1ed3 th\u1ecb (C).<\/p>\n

a) $\\lim_{x \\to -\\infty} f(x) = -\\infty$.
\nb) \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 $f'(x) = -8x^3 + 8x + 1$.
\nc) T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $f'(x)=0$ l\u00e0 $S = \\{-1; 0; 1\\}$.
\nd) Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a $f(x)$ l\u00e0 1.<\/p>\n

C\u00c2U 3: \u1ee8ng d\u1ee5ng c\u1ee7a h\u00e0m s\u1ed1 trong b\u00e0i to\u00e1n th\u1ef1c t\u1ebf (t\u1ed1i \u01b0u l\u1ee3i nhu\u1eadn)<\/strong><\/p>\n

V\u00ed d\u1ee5 1:<\/strong> M\u1ed9t doanh nghi\u1ec7p d\u1ef1 \u0111\u1ecbnh s\u1ea3n xu\u1ea5t x s\u1ea3n ph\u1ea9m ($x \\in \\mathbb{N}, 0 \\le x \\le 1100$) th\u00ec doanh thu nh\u1eadn \u0111\u01b0\u1ee3c khi b\u00e1n h\u1ebft s\u1ed1 s\u1ea3n ph\u1ea9m \u0111\u00f3 l\u00e0 $F(x) = x^3 \u2013 2199x^2 + 1219000x + 2025000$ (\u0111\u1ed3ng), trong khi chi ph\u00ed s\u1ea3n xu\u1ea5t b\u00ecnh qu\u00e2n cho m\u1ed9t s\u1ea3n ph\u1ea9m l\u00e0 $G(x) = x + 9000 + \\frac{2025000}{x}$ (\u0111\u1ed3ng). Gi\u1ea3 s\u1eed s\u1ed1 s\u1ea3n ph\u1ea9m s\u1ea3n xu\u1ea5t ra lu\u00f4n \u0111\u01b0\u1ee3c b\u00e1n h\u1ebft, S\u1ed1 s\u1ea3n ph\u1ea9m t\u1ed1i \u0111a m\u00e0 doanh nghi\u1ec7p c\u00f3 th\u1ec3 s\u1ea3n xu\u1ea5t l\u00e0 bao nhi\u00eau \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o l\u1ee3i nhu\u1eadn l\u1edbn h\u01a1n 150 tri\u1ec7u \u0111\u1ed3ng?<\/p>\n

T\u1ea3i B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/strong><\/h2>\n

B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/strong><\/a> cung c\u1ea5p m\u1ed9t c\u00e1i nh\u00ecn t\u1ed5ng quan v\u00e0 s\u00e2u s\u1eafc v\u1ec1 c\u00e1c d\u1ea1ng b\u00e0i h\u00e0m s\u1ed1 th\u01b0\u1eddng g\u1eb7p trong \u0111\u1ec1 thi THPTQG, gi\u00fap h\u1ecdc sinh luy\u1ec7n t\u1eadp v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n hi\u1ec7u qu\u1ea3. T\u1ea3i ngay file qua \u0111\u01b0\u1eddng link b\u00ean d\u01b0\u1edbi nh\u00e9!<\/p>\n

T\u1ea3i B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

B\u1ed9 c\u00e2u h\u1ecfi H\u00e0m S\u1ed1 ph\u00e1t tri\u1ec3n t\u1eeb \u0111\u1ec1 thi THPTQG Anh Gi\u00e1o Kid c\u00f3 c\u1ea5u tr\u00fac v\u00e0 d\u1ea1ng b\u00e0i c\u1ee7a \u0111\u1ec1 thi THPTQG ch\u00ednh th\u1ee9c. T\u00e0i li\u1ec7u t\u1eadp trung v\u00e0o chuy\u00ean \u0111\u1ec1 H\u00e0m S\u1ed1 v\u1edbi c\u00e1c c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i r\u00f5 r\u00e0ng, t\u1eeb nh\u1eadn bi\u1ebft \u0111\u1ebfn v\u1eadn d\u1ee5ng cao. Ngo\u00e0i ra, b\u1ed9 c\u00e2u […]\n","protected":false},"author":1,"featured_media":1970,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[78,10],"class_list":["post-772","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-12","tag-anh-giao-kid","tag-toan-12"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=772"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/772\/revisions"}],"predecessor-version":[{"id":1971,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/772\/revisions\/1971"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1970"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}