{"id":568957,"date":"2026-07-24T09:30:11","date_gmt":"2026-07-24T02:30:11","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=568957"},"modified":"2026-07-24T09:35:44","modified_gmt":"2026-07-24T02:35:44","slug":"tinh-don-dieu-cua-ham-so","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/tinh-don-dieu-cua-ham-so\/","title":{"rendered":"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch x\u00e9t \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn"},"content":{"rendered":"<p>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 t\u00ednh ch\u1ea5t \u0111\u1ed3ng bi\u1ebfn (t\u0103ng) ho\u1eb7c ngh\u1ecbch bi\u1ebfn (gi\u1ea3m) c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t kho\u1ea3ng x\u00e1c \u0111\u1ecbnh: h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn khi gi\u00e1 tr\u1ecb y t\u0103ng theo x, ngh\u1ecbch bi\u1ebfn khi gi\u00e1 tr\u1ecb y gi\u1ea3m d\u1ea7n khi x t\u0103ng. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n c\u1ee7a Gi\u1ea3i t\u00edch l\u1edbp 12, xu\u1ea5t hi\u1ec7n g\u1ea7n nh\u01b0 trong m\u1ecdi b\u00e0i kh\u1ea3o s\u00e1t v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. C\u00f4ng c\u1ee5 quan tr\u1ecdng nh\u1ea5t \u0111\u1ec3 x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u ch\u00ednh l\u00e0 d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m f'(x). Khi n\u1eafm ch\u1eafc m\u1ed1i li\u00ean h\u1ec7 n\u00e0y c\u00f9ng c\u00e1ch l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean, b\u1ea1n s\u1ebd t\u00ecm nhanh c\u00e1c kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn v\u00e0 gi\u1ea3i g\u1ecdn nhi\u1ec1u d\u1ea1ng b\u00e0i tr\u1eafc nghi\u1ec7m.<\/p>\n<h2>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/h2>\n<p>Cho h\u00e0m s\u1ed1 y = f(x) x\u00e1c \u0111\u1ecbnh tr\u00ean kho\u1ea3ng K (K c\u00f3 th\u1ec3 l\u00e0 kho\u1ea3ng, n\u1eeda kho\u1ea3ng ho\u1eb7c \u0111o\u1ea1n). Ta c\u00f3 hai kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n:<\/p>\n<ul>\n<li>H\u00e0m s\u1ed1 <strong>\u0111\u1ed3ng bi\u1ebfn<\/strong> (t\u0103ng) tr\u00ean K n\u1ebfu v\u1edbi m\u1ecdi x\u2081, x\u2082 thu\u1ed9c K m\u00e0 x\u2081 &lt; x\u2082 th\u00ec f(x\u2081) &lt; f(x\u2082). N\u00f3i c\u00e1ch kh\u00e1c, khi x t\u0103ng th\u00ec y c\u0169ng t\u0103ng.<\/li>\n<li>H\u00e0m s\u1ed1 <strong>ngh\u1ecbch bi\u1ebfn<\/strong> (gi\u1ea3m) tr\u00ean K n\u1ebfu v\u1edbi m\u1ecdi x\u2081, x\u2082 thu\u1ed9c K m\u00e0 x\u2081 &lt; x\u2082 th\u00ec f(x\u2081) &gt; f(x\u2082). T\u1ee9c l\u00e0 khi x t\u0103ng th\u00ec y gi\u1ea3m.<\/li>\n<\/ul>\n<p>H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean K \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 h\u00e0m s\u1ed1 <strong>\u0111\u01a1n \u0111i\u1ec7u<\/strong> tr\u00ean K. Vi\u1ec7c t\u00ecm c\u00e1c kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u00ecm chi\u1ec1u bi\u1ebfn thi\u00ean hay x\u00e9t kho\u1ea3ng \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1. B\u1ea1n c\u00f3 th\u1ec3 xem l\u1ea1i kh\u00e1i ni\u1ec7m n\u1ec1n \u1edf b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-la-gi\/\">h\u00e0m s\u1ed1 l\u00e0 g\u00ec<\/a>. V\u1ec1 m\u1eb7t h\u00ecnh h\u1ecdc, tr\u00ean kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn \u0111\u1ed3 th\u1ecb \u0111i l\u00ean t\u1eeb tr\u00e1i sang ph\u1ea3i, c\u00f2n tr\u00ean kho\u1ea3ng ngh\u1ecbch bi\u1ebfn \u0111\u1ed3 th\u1ecb \u0111i xu\u1ed1ng.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-569641 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-1.jpg\" alt=\"tinh-don-dieu-cua-ham-so-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa t\u00ednh \u0111\u01a1n \u0111i\u1ec7u v\u00e0 \u0111\u1ea1o h\u00e0m<\/h2>\n<p>\u0110\u1ecbnh l\u00fd c\u01a1 b\u1ea3n d\u00f9ng \u0111\u1ec3 x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u d\u1ef1a ho\u00e0n to\u00e0n v\u00e0o d\u1ea5u c\u1ee7a <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dao-ham-lop-11\/\">\u0111\u1ea1o h\u00e0m<\/a>. Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ea1o h\u00e0m tr\u00ean kho\u1ea3ng K, khi \u0111\u00f3 d\u1ea5u c\u1ee7a f'(x) quy\u1ebft \u0111\u1ecbnh chi\u1ec1u bi\u1ebfn thi\u00ean nh\u01b0 b\u1ea3ng sau.<\/p>\n<table>\n<thead>\n<tr>\n<th>D\u1ea5u c\u1ee7a f'(x) tr\u00ean K<\/th>\n<th>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>f'(x) &gt; 0 v\u1edbi m\u1ecdi x thu\u1ed9c K<\/td>\n<td>H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean K<\/td>\n<\/tr>\n<tr>\n<td>f'(x) &lt; 0 v\u1edbi m\u1ecdi x thu\u1ed9c K<\/td>\n<td>H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean K<\/td>\n<\/tr>\n<tr>\n<td>f'(x) = 0 v\u1edbi m\u1ecdi x thu\u1ed9c K<\/td>\n<td>H\u00e0m s\u1ed1 kh\u00f4ng \u0111\u1ed5i (h\u1eb1ng s\u1ed1) tr\u00ean K<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>M\u1ed9t \u0111i\u1ec3m c\u1ea7n nh\u1edb: \u0111\u1ecbnh l\u00fd m\u1edf r\u1ed9ng cho ph\u00e9p f'(x) = 0 t\u1ea1i m\u1ed9t s\u1ed1 <em>h\u1eefu h\u1ea1n<\/em> \u0111i\u1ec3m m\u00e0 t\u00ednh \u0111\u01a1n \u0111i\u1ec7u v\u1eabn \u0111\u01b0\u1ee3c b\u1ea3o to\u00e0n. C\u1ee5 th\u1ec3, n\u1ebfu f'(x) \u2265 0 tr\u00ean K v\u00e0 ch\u1ec9 b\u1eb1ng 0 t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m th\u00ec h\u00e0m s\u1ed1 v\u1eabn \u0111\u1ed3ng bi\u1ebfn tr\u00ean K; t\u01b0\u01a1ng t\u1ef1 v\u1edbi f'(x) \u2264 0 th\u00ec h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn. \u0110\u00e2y l\u00e0 l\u00fd do h\u00e0m y = x\u00b3 v\u1eabn \u0111\u1ed3ng bi\u1ebfn tr\u00ean to\u00e0n b\u1ed9 R d\u00f9 c\u00f3 y'(0) = 0.<\/p>\n<h2>C\u00e1c b\u01b0\u1edbc x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/h2>\n<p>Quy tr\u00ecnh chu\u1ea9n \u0111\u1ec3 x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u g\u1ed3m b\u1ed1n b\u01b0\u1edbc, \u00e1p d\u1ee5ng cho h\u1ea7u h\u1ebft d\u1ea1ng h\u00e0m trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 12.<\/p>\n<ul>\n<li><strong>B\u01b0\u1edbc 1:<\/strong> T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh D c\u1ee7a h\u00e0m s\u1ed1. V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c, c\u0103n th\u1ee9c c\u1ea7n lo\u1ea1i c\u00e1c \u0111i\u1ec3m l\u00e0m m\u1eabu b\u1eb1ng 0 ho\u1eb7c bi\u1ec3u th\u1ee9c d\u01b0\u1edbi c\u0103n \u00e2m.<\/li>\n<li><strong>B\u01b0\u1edbc 2:<\/strong> T\u00ednh \u0111\u1ea1o h\u00e0m f'(x). T\u00ecm c\u00e1c \u0111i\u1ec3m m\u00e0 f'(x) = 0 ho\u1eb7c f'(x) kh\u00f4ng x\u00e1c \u0111\u1ecbnh (c\u00e1c \u0111i\u1ec3m t\u1edbi h\u1ea1n).<\/li>\n<li><strong>B\u01b0\u1edbc 3:<\/strong> S\u1eafp x\u1ebfp c\u00e1c \u0111i\u1ec3m t\u1edbi h\u1ea1n theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n v\u00e0 l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean, x\u00e9t d\u1ea5u f'(x) tr\u00ean t\u1eebng kho\u1ea3ng.<\/li>\n<li><strong>B\u01b0\u1edbc 4:<\/strong> D\u1ef1a v\u00e0o d\u1ea5u c\u1ee7a f'(x) tr\u00ean m\u1ed7i kho\u1ea3ng \u0111\u1ec3 k\u1ebft lu\u1eadn kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn (f&#8217; &gt; 0) v\u00e0 kho\u1ea3ng ngh\u1ecbch bi\u1ebfn (f&#8217; &lt; 0).<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"size-full wp-image-569642 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-2.jpg\" alt=\"tinh-don-dieu-cua-ham-so-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u1ea3ng bi\u1ebfn thi\u00ean m\u1eabu<\/h2>\n<p>B\u1ea3ng bi\u1ebfn thi\u00ean l\u00e0 c\u00f4ng c\u1ee5 tr\u1ef1c quan \u0111\u1ec3 t\u1ed5ng h\u1ee3p d\u1ea5u \u0111\u1ea1o h\u00e0m v\u00e0 chi\u1ec1u bi\u1ebfn thi\u00ean. V\u1edbi h\u00e0m b\u1eadc ba y = x\u00b3 \u2212 3x c\u00f3 \u0111\u1ea1o h\u00e0m y&#8217; = 3x\u00b2 \u2212 3 = 3(x \u2212 1)(x + 1), nghi\u1ec7m y&#8217; = 0 l\u00e0 x = \u22121 v\u00e0 x = 1. X\u00e9t d\u1ea5u tr\u00ean tr\u1ee5c s\u1ed1, b\u1ea3ng bi\u1ebfn thi\u00ean r\u00fat g\u1ecdn nh\u01b0 sau:<\/p>\n<table>\n<thead>\n<tr>\n<th>Kho\u1ea3ng<\/th>\n<th>(\u2212\u221e; \u22121)<\/th>\n<th>(\u22121; 1)<\/th>\n<th>(1; +\u221e)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>D\u1ea5u c\u1ee7a y&#8217;<\/td>\n<td>+<\/td>\n<td>\u2212<\/td>\n<td>+<\/td>\n<\/tr>\n<tr>\n<td>Chi\u1ec1u bi\u1ebfn thi\u00ean<\/td>\n<td>\u0110\u1ed3ng bi\u1ebfn<\/td>\n<td>Ngh\u1ecbch bi\u1ebfn<\/td>\n<td>\u0110\u1ed3ng bi\u1ebfn<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>T\u1eeb b\u1ea3ng, h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean (\u2212\u221e; \u22121) v\u00e0 (1; +\u221e), ngh\u1ecbch bi\u1ebfn tr\u00ean (\u22121; 1). \u0110i\u1ec3m x = \u22121 l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i, x = 1 l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u.<\/p>\n<h2>V\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft<\/h2>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 ba v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh theo \u0111\u00fang b\u1ed1n b\u01b0\u1edbc \u1edf tr\u00ean, \u0111i t\u1eeb h\u00e0m b\u1eadc hai \u0111\u1ebfn b\u1eadc ba v\u00e0 ph\u00e2n th\u1ee9c.<\/p>\n<h3>V\u00ed d\u1ee5 1: H\u00e0m b\u1eadc hai y = x\u00b2 \u2212 4x + 1<\/h3>\n<ul>\n<li>B\u01b0\u1edbc 1: T\u1eadp x\u00e1c \u0111\u1ecbnh D = R.<\/li>\n<li>B\u01b0\u1edbc 2: y&#8217; = 2x \u2212 4; y&#8217; = 0 khi x = 2.<\/li>\n<li>B\u01b0\u1edbc 3 &amp; 4: V\u1edbi x &lt; 2 th\u00ec y&#8217; &lt; 0 n\u00ean h\u00e0m ngh\u1ecbch bi\u1ebfn tr\u00ean (\u2212\u221e; 2); v\u1edbi x &gt; 2 th\u00ec y&#8217; &gt; 0 n\u00ean h\u00e0m \u0111\u1ed3ng bi\u1ebfn tr\u00ean (2; +\u221e). \u0110i\u1ec3m x = 2 l\u00e0 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u v\u1edbi y = \u22123.<\/li>\n<\/ul>\n<h3>V\u00ed d\u1ee5 2: H\u00e0m b\u1eadc ba y = x\u00b3 \u2212 3x<\/h3>\n<ul>\n<li>B\u01b0\u1edbc 1: T\u1eadp x\u00e1c \u0111\u1ecbnh D = R.<\/li>\n<li>B\u01b0\u1edbc 2: y&#8217; = 3x\u00b2 \u2212 3 = 3(x \u2212 1)(x + 1); y&#8217; = 0 khi x = \u22121 ho\u1eb7c x = 1.<\/li>\n<li>B\u01b0\u1edbc 3 &amp; 4: Theo b\u1ea3ng bi\u1ebfn thi\u00ean \u1edf tr\u00ean, h\u00e0m \u0111\u1ed3ng bi\u1ebfn tr\u00ean (\u2212\u221e; \u22121) v\u00e0 (1; +\u221e), ngh\u1ecbch bi\u1ebfn tr\u00ean (\u22121; 1). \u0110\u00e2y l\u00e0 d\u1ea1ng \u0111\u1ed3 th\u1ecb b\u1eadc ba c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb quen thu\u1ed9c.<\/li>\n<\/ul>\n<h3>V\u00ed d\u1ee5 3: H\u00e0m ph\u00e2n th\u1ee9c y = (x \u2212 1)\/(x + 2)<\/h3>\n<ul>\n<li>B\u01b0\u1edbc 1: T\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\ {\u22122} (lo\u1ea1i x = \u22122 v\u00ec l\u00e0m m\u1eabu b\u1eb1ng 0).<\/li>\n<li>B\u01b0\u1edbc 2: y&#8217; = 3\/(x + 2)\u00b2 &gt; 0 v\u1edbi m\u1ecdi x \u2260 \u22122.<\/li>\n<li>B\u01b0\u1edbc 3 &amp; 4: \u0110\u1ea1o h\u00e0m lu\u00f4n d\u01b0\u01a1ng n\u00ean h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng (\u2212\u221e; \u22122) v\u00e0 (\u22122; +\u221e). L\u01b0u \u00fd kh\u00f4ng \u0111\u01b0\u1ee3c k\u1ebft lu\u1eadn h\u00e0m \u0111\u1ed3ng bi\u1ebfn tr\u00ean R v\u00ec h\u00e0m b\u1ecb gi\u00e1n \u0111o\u1ea1n t\u1ea1i x = \u22122 (\u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng).<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"size-full wp-image-569643 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-3.jpg\" alt=\"tinh-don-dieu-cua-ham-so-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u01b0u \u00fd quan tr\u1ecdng khi x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u<\/h2>\n<p>M\u1ed9t v\u00e0i l\u1ed7i th\u01b0\u1eddng g\u1eb7p khi\u1ebfn k\u1ebft lu\u1eadn sai l\u1ec7ch c\u1ea7n tr\u00e1nh:<\/p>\n<ul>\n<li>Ch\u1ec9 \u0111\u01b0\u1ee3c k\u1ebft lu\u1eadn \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean <strong>t\u1eebng kho\u1ea3ng<\/strong> c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh, kh\u00f4ng g\u1ed9p hai kho\u1ea3ng r\u1eddi nhau b\u1eb1ng d\u1ea5u &#8220;v\u00e0&#8221; th\u00e0nh m\u1ed9t kho\u1ea3ng n\u1ed1i b\u1eb1ng d\u1ea5u &#8220;\u222a&#8221;.<\/li>\n<li>V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c hay h\u00e0m c\u00f3 \u0111i\u1ec3m gi\u00e1n \u0111o\u1ea1n, ph\u1ea3i lo\u1ea1i \u0111i\u1ec3m kh\u00f4ng thu\u1ed9c t\u1eadp x\u00e1c \u0111\u1ecbnh tr\u01b0\u1edbc khi x\u00e9t d\u1ea5u.<\/li>\n<li>D\u1ea5u b\u1eb1ng c\u1ee7a f'(x) ch\u1ec9 \u0111\u01b0\u1ee3c ph\u00e9p x\u1ea3y ra t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m; n\u1ebfu f'(x) = 0 tr\u00ean c\u1ea3 m\u1ed9t kho\u1ea3ng th\u00ec h\u00e0m l\u00e0 h\u1eb1ng s\u1ed1, kh\u00f4ng ph\u1ea3i \u0111\u01a1n \u0111i\u1ec7u.<\/li>\n<li>Khi \u0111\u1ec1 cho tham s\u1ed1 m, \u0111i\u1ec1u ki\u1ec7n \u0111\u1ed3ng bi\u1ebfn tr\u00ean R c\u1ee7a h\u00e0m b\u1eadc ba th\u01b0\u1eddng quy v\u1ec1 f'(x) \u2265 0 v\u1edbi m\u1ecdi x, t\u1ee9c bi\u1ec7t th\u1ee9c c\u1ee7a f'(x) kh\u00f4ng d\u01b0\u01a1ng.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-569644 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-4.jpg\" alt=\"tinh-don-dieu-cua-ham-so-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/tinh-don-dieu-cua-ham-so-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/h2>\n<h3>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 t\u00ednh \u0111\u1ed3ng bi\u1ebfn (t\u0103ng) ho\u1eb7c ngh\u1ecbch bi\u1ebfn (gi\u1ea3m) c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t kho\u1ea3ng x\u00e1c \u0111\u1ecbnh. H\u00e0m \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean K \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 h\u00e0m \u0111\u01a1n \u0111i\u1ec7u tr\u00ean K.<\/p>\n<h3>Khi n\u00e0o h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn, khi n\u00e0o ngh\u1ecbch bi\u1ebfn?<\/h3>\n<p>H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean K khi f'(x) &gt; 0 v\u1edbi m\u1ecdi x thu\u1ed9c K, v\u00e0 ngh\u1ecbch bi\u1ebfn khi f'(x) &lt; 0 v\u1edbi m\u1ecdi x thu\u1ed9c K (d\u1ea5u b\u1eb1ng ch\u1ec9 \u0111\u01b0\u1ee3c x\u1ea3y ra t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m).<\/p>\n<h3>X\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 b\u1eb1ng c\u00e1ch n\u00e0o?<\/h3>\n<p>Th\u1ef1c hi\u1ec7n b\u1ed1n b\u01b0\u1edbc: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m f'(x), l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean x\u00e9t d\u1ea5u f'(x), r\u1ed3i k\u1ebft lu\u1eadn kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn v\u00e0 ngh\u1ecbch bi\u1ebfn.<\/p>\n<h3>H\u00e0m s\u1ed1 y = x\u00b3 \u0111\u1ed3ng bi\u1ebfn hay ngh\u1ecbch bi\u1ebfn tr\u00ean R?<\/h3>\n<p>\u0110\u1ed3ng bi\u1ebfn tr\u00ean R. V\u00ec y&#8217; = 3x\u00b2 \u2265 0 v\u1edbi m\u1ecdi x v\u00e0 ch\u1ec9 b\u1eb1ng 0 t\u1ea1i m\u1ed9t \u0111i\u1ec3m x = 0 n\u00ean h\u00e0m s\u1ed1 v\u1eabn \u0111\u1ed3ng bi\u1ebfn tr\u00ean to\u00e0n t\u1eadp s\u1ed1 th\u1ef1c.<\/p>\n<h3>V\u00ec sao h\u00e0m ph\u00e2n th\u1ee9c kh\u00f4ng k\u1ebft lu\u1eadn \u0111\u01a1n \u0111i\u1ec7u tr\u00ean R?<\/h3>\n<p>V\u00ec h\u00e0m b\u1ecb gi\u00e1n \u0111o\u1ea1n t\u1ea1i \u0111i\u1ec3m l\u00e0m m\u1eabu b\u1eb1ng 0 (ti\u1ec7m c\u1eadn \u0111\u1ee9ng). Ta ch\u1ec9 k\u1ebft lu\u1eadn \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh, kh\u00f4ng n\u1ed1i hai kho\u1ea3ng qua \u0111i\u1ec3m gi\u00e1n \u0111o\u1ea1n.<\/p>\n<h3>\u0110i\u1ec3m m\u00e0 f'(x) = 0 c\u00f3 \u00fd ngh\u0129a g\u00ec?<\/h3>\n<p>\u0110\u00f3 l\u00e0 \u0111i\u1ec3m t\u1edbi h\u1ea1n, n\u01a1i h\u00e0m s\u1ed1 c\u00f3 th\u1ec3 \u0111\u1ed5i chi\u1ec1u bi\u1ebfn thi\u00ean. N\u1ebfu f'(x) \u0111\u1ed5i d\u1ea5u qua \u0111i\u1ec3m n\u00e0y th\u00ec \u0111\u00f3 l\u00e0 \u0111i\u1ec3m c\u1ef1c tr\u1ecb (c\u1ef1c \u0111\u1ea1i ho\u1eb7c c\u1ef1c ti\u1ec3u) c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n<h3>B\u1ea3ng bi\u1ebfn thi\u00ean d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>B\u1ea3ng bi\u1ebfn thi\u00ean t\u1ed5ng h\u1ee3p tr\u1ef1c quan d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m, chi\u1ec1u bi\u1ebfn thi\u00ean v\u00e0 gi\u00e1 tr\u1ecb c\u1ef1c tr\u1ecb, gi\u00fap b\u1ea1n \u0111\u1ecdc nhanh kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ch\u00ednh x\u00e1c.<\/p>\n<p><script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L\u00e0 t\u00ednh \u0111\u1ed3ng bi\u1ebfn (t\u0103ng) ho\u1eb7c ngh\u1ecbch bi\u1ebfn (gi\u1ea3m) c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t kho\u1ea3ng x\u00e1c \u0111\u1ecbnh. H\u00e0m \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean K \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 h\u00e0m \u0111\u01a1n \u0111i\u1ec7u tr\u00ean K.\"}},{\"@type\":\"Question\",\"name\":\"Khi n\u00e0o h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn, khi n\u00e0o ngh\u1ecbch bi\u1ebfn?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean K khi f'(x) > 0 v\u1edbi m\u1ecdi x thu\u1ed9c K, v\u00e0 ngh\u1ecbch bi\u1ebfn khi f'(x) < 0 v\u1edbi m\u1ecdi x thu\u1ed9c K, d\u1ea5u b\u1eb1ng ch\u1ec9 \u0111\u01b0\u1ee3c x\u1ea3y ra t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m.\"}},{\"@type\":\"Question\",\"name\":\"X\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 b\u1eb1ng c\u00e1ch n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Th\u1ef1c hi\u1ec7n b\u1ed1n b\u01b0\u1edbc: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m f'(x), l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean x\u00e9t d\u1ea5u f'(x), r\u1ed3i k\u1ebft lu\u1eadn kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn v\u00e0 ngh\u1ecbch bi\u1ebfn.\"}},{\"@type\":\"Question\",\"name\":\"H\u00e0m s\u1ed1 y = x^3 \u0111\u1ed3ng bi\u1ebfn hay ngh\u1ecbch bi\u1ebfn tr\u00ean R?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u1ed3ng bi\u1ebfn tr\u00ean R. V\u00ec y' = 3x^2 \u2265 0 v\u1edbi m\u1ecdi x v\u00e0 ch\u1ec9 b\u1eb1ng 0 t\u1ea1i m\u1ed9t \u0111i\u1ec3m x = 0 n\u00ean h\u00e0m s\u1ed1 v\u1eabn \u0111\u1ed3ng bi\u1ebfn tr\u00ean to\u00e0n t\u1eadp s\u1ed1 th\u1ef1c.\"}},{\"@type\":\"Question\",\"name\":\"V\u00ec sao h\u00e0m ph\u00e2n th\u1ee9c kh\u00f4ng k\u1ebft lu\u1eadn \u0111\u01a1n \u0111i\u1ec7u tr\u00ean R?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"V\u00ec h\u00e0m b\u1ecb gi\u00e1n \u0111o\u1ea1n t\u1ea1i \u0111i\u1ec3m l\u00e0m m\u1eabu b\u1eb1ng 0 (ti\u1ec7m c\u1eadn \u0111\u1ee9ng). Ta ch\u1ec9 k\u1ebft lu\u1eadn \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh.\"}},{\"@type\":\"Question\",\"name\":\"\u0110i\u1ec3m m\u00e0 f'(x) = 0 c\u00f3 \u00fd ngh\u0129a g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u00f3 l\u00e0 \u0111i\u1ec3m t\u1edbi h\u1ea1n, n\u01a1i h\u00e0m s\u1ed1 c\u00f3 th\u1ec3 \u0111\u1ed5i chi\u1ec1u bi\u1ebfn thi\u00ean. N\u1ebfu f'(x) \u0111\u1ed5i d\u1ea5u qua \u0111i\u1ec3m n\u00e0y th\u00ec \u0111\u00f3 l\u00e0 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1.\"}},{\"@type\":\"Question\",\"name\":\"B\u1ea3ng bi\u1ebfn thi\u00ean d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"B\u1ea3ng bi\u1ebfn thi\u00ean t\u1ed5ng h\u1ee3p d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m, chi\u1ec1u bi\u1ebfn thi\u00ean v\u00e0 gi\u00e1 tr\u1ecb c\u1ef1c tr\u1ecb, gi\u00fap \u0111\u1ecdc nhanh kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ch\u00ednh x\u00e1c.\"}}]}\n<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 t\u00ednh \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c ngh\u1ecbch bi\u1ebfn, \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh qua d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m: f'(x) &gt; 0 th\u00ec \u0111\u1ed3ng bi\u1ebfn, f'(x) &lt; 0 th\u00ec ngh\u1ecbch bi\u1ebfn. N\u1eafm v\u1eefng b\u1ed1n b\u01b0\u1edbc x\u00e9t d\u1ea5u v\u00e0 c\u00e1ch l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i nhanh c\u00e1c b\u00e0i kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1. B\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam nhi\u1ec1u b\u00e0i To\u00e1n v\u00e0 m\u1eb9o h\u1ecdc t\u1eadp kh\u00e1c tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile \u0111\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 t\u00ednh ch\u1ea5t \u0111\u1ed3ng bi\u1ebfn (t\u0103ng) ho\u1eb7c ngh\u1ecbch bi\u1ebfn (gi\u1ea3m) c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t kho\u1ea3ng x\u00e1c \u0111\u1ecbnh: h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn khi gi\u00e1 tr\u1ecb y t\u0103ng theo x, ngh\u1ecbch bi\u1ebfn khi gi\u00e1 tr\u1ecb y gi\u1ea3m d\u1ea7n khi x t\u0103ng. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n c\u1ee7a Gi\u1ea3i t\u00edch l\u1edbp [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":569640,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1","_yoast_wpseo_title":"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1: \u0110\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn","_yoast_wpseo_metadesc":"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? H\u01b0\u1edbng d\u1eabn c\u00e1ch x\u00e9t \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn qua d\u1ea5u \u0111\u1ea1o h\u00e0m, l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft. Xem ngay!","footnotes":""},"categories":[29235,3910,30453],"tags":[],"class_list":["post-568957","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-goc-to-mo","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1: \u0110\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn<\/title>\n<meta name=\"description\" content=\"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? H\u01b0\u1edbng d\u1eabn c\u00e1ch x\u00e9t \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn qua d\u1ea5u \u0111\u1ea1o h\u00e0m, l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft. Xem ngay!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tinh-don-dieu-cua-ham-so\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch x\u00e9t \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn\" \/>\n<meta property=\"og:description\" content=\"T\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec? H\u01b0\u1edbng d\u1eabn c\u00e1ch x\u00e9t \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn qua d\u1ea5u \u0111\u1ea1o h\u00e0m, l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft. 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