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{"id":21527,"date":"2018-03-15T22:34:58","date_gmt":"2018-03-15T15:34:58","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=21527"},"modified":"2018-03-15T22:34:58","modified_gmt":"2018-03-15T15:34:58","slug":"giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so\/","title":{"rendered":"Gi\u1ea3i t\u00edch – Ch\u01b0\u01a1ng 1 – B\u00e0i 1: S\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1"},"content":{"rendered":"

B\u00e0i 1 (trang 9 SGK Gi\u1ea3i t\u00edch 12):\u00a0X\u00e9t s\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1:<\/strong><\/span><\/p>\n

a) y = 4 + 3x \u2013 x2<\/sup><\/p>\n

\"\"<\/p>\n

c) y = x4 – 2×2 + 3<\/p>\n

d) y = -x3 + x2 \u2013 5<\/p>\n

L\u1eddi gi\u1ea3i:<\/strong><\/p>\n

(L\u01b0u \u00fd:<\/strong><\/p>\n

\u0110\u1ec3 x\u00e9t xem d\u1ea5u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 + hay – trong m\u1ed9t kho\u1ea3ng n\u00e0o \u0111\u00f3 \u1edf b\u1ea3ng bi\u1ebfn thi\u00ean, b\u1ea1n l\u1ea5y m\u1ed9t gi\u00e1 tr\u1ecb b\u1ea5t k\u00ec n\u1eb1m trong kho\u1ea3ng \u0111\u00f3, thay v\u00e0o \u0111\u1ea1o h\u00e0m y’. N\u1ebfu y’ l\u00e0 d\u01b0\u01a1ng th\u00ec d\u1ea5u c\u1ee7a y’ trong kho\u1ea3ng \u0111\u00f3 l\u00e0 + v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/em><\/p>\n

V\u00ed d\u1ee5: x\u00e9t d\u1ea5u y’ = -x2 + 4 trong kho\u1ea3ng (-2; 2). Ch\u1eb3ng h\u1ea1n ta l\u1ea5y m\u1ed9t gi\u00e1 tr\u1ecb b\u1ea5t k\u00ec trong kho\u1ea3ng l\u00e0 1, thay v\u00e0o y’ ta \u0111\u01b0\u1ee3c: y’ = -(-1)2 + 4 = 3 > 0. Do \u0111\u00f3 d\u1ea5u c\u1ee7a y’ trong kho\u1ea3ng (-2; 2) s\u1ebd l\u00e0 +.)<\/em><\/p>\n

a)<\/b>\u00a0D = R<\/p>\n

y’ = 3 \u2013 2x = 0 \u21d4 x = 3\/2<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn trong kho\u1ea3ng (-\u221e; 3\/2 ) v\u00e0 ngh\u1ecbch bi\u1ebfn trong kho\u1ea3ng ( 3\/2 ; + \u221e ).<\/p>\n

b)<\/b>\u00a0D = R<\/p>\n

y’ = x2<\/sup>\u00a0+ 6x – 7<\/p>\n

y’ = 0 \u21d4 x = -7 ho\u1eb7c x = 1<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-\u221e ; -7) v\u00e0 (1 ; +\u221e ); ngh\u1ecbch bi\u1ebfn trong kho\u1ea3ng (-7; 1 ).<\/p>\n

c)<\/b>\u00a0D = R<\/p>\n

y’= 4x3<\/sup>\u00a0– 4x = 4x(x2<\/sup>\u00a0– 1)<\/p>\n

y’ = 0 \u21d4 x = 0 ho\u1eb7c x = 1 ho\u1eb7c x = -1<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-\u221e ; 1) v\u00e0 (0 ; 1); \u0111\u1ed3ng bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-1 ; 0) v\u00e0 ( 1; +\u221e).<\/p>\n

d)<\/b>\u00a0D = R<\/p>\n

y’= -3x2<\/sub>\u00a0+ 2x<\/p>\n

y’ = 0 \u21d4 x = 0 ho\u1eb7c x = 2\/3<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-\u221e ; 0) v\u00e0 (2\/3 ; + \u221e), \u0111\u1ed3ng bi\u1ebfn trong kho\u1ea3ng (0 ; 2\/3 ).<\/p>\n

\n

B\u00e0i 2 (trang 10 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ecm c\u00e1c kho\u1ea3ng \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a c\u00e1c h\u00e0m s\u1ed1:<\/strong><\/span><\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\n

a)<\/b>\u00a0D = R \\ {1}<\/p>\n

\"\"<\/p>\n

y’ kh\u00f4ng x\u00e1c \u0111\u1ecbnh t\u1ea1i x = 1<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n<\/div>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-\u221e ; 1) v\u00e0 (1 ; +\u221e ) .<\/p>\n

b)<\/b>\u00a0D = R \\ {1}<\/p>\n

\"\"<\/p>\n<\/div>\n

y’ kh\u00f4ng x\u00e1c \u0111\u1ecbnh t\u1ea1i x = 1<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong c\u00e1c kho\u1ea3ng (-\u221e ;1) v\u00e0 (1 ; +\u221e)<\/p>\n

\"\"<\/p>\n

c)<\/b>\u00a0D = (-\u221e ; -4] \u222a [5; +\u221e)<\/p>\n

\"\"<\/p>\n

y’ kh\u00f4ng x\u00e1c \u0111\u1ecbnh t\u1ea1i x = -4 v\u00e0 x = 5<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong n\u1eeda kho\u1ea3ng (-\u221e ; -4] v\u00e0 \u0111\u1ed3ng bi\u1ebfn trong n\u1eeda kho\u1ea3ng [5 ; + \u221e ).<\/p>\n

d)<\/b>\u00a0D = R \\ {\u00b13}<\/p>\n

\"\"<\/p>\n

y’ kh\u00f4ng x\u00e1c \u0111\u1ecbnh t\u1ea1i x = \u00b13<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong c\u00e1c kho\u1ea3ng \u0111\u00f3 n\u00ean h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong kho\u1ea3ng (-\u221e ; -3) ( -3; 3) v\u00e0 (3; +\u221e )<\/p>\n

\n

B\u00e0i 3 (trang 10 SGK Gi\u1ea3i t\u00edch 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

\"\"<\/p>\n

\u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-1; 1), ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; -1) v\u00e0 (1; +\u221e).<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

TX\u0110: D = R<\/p>\n

\"\"<\/p>\n

y’ = 0 => x = \u00b11<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-1; 1), ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; -1) v\u00e0 (1; +\u221e) (\u0111pcm).<\/p>\n

\n
\n

B\u00e0i 4 (trang 10 SGK Gi\u1ea3i t\u00edch 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

\"\"<\/p>\n

\n

\u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (0; 1), ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (1; 2).<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

TX\u0110: D = [0; 2]<\/p>\n

\"\"<\/p>\n

\n

y’ = 0 => x = 1<\/p>\n

B\u1ea3ng x\u00e9t d\u1ea5u y’:<\/p>\n

\"\"<\/p>\n

T\u1eeb b\u1ea3ng tr\u00ean ta c\u00f3:<\/p>\n

+ y’ > 0 v\u1edbi x \u2208 (0; 1) do \u0111\u00f3 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3n (0; 1);<\/p>\n

+ y’ < 0 v\u1edbi x \u2208 (1; 2) n\u00ean ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (1; 2).<\/p>\n

V\u1eady h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (0; 1), ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (1; 2) (\u0111pcm).<\/p>\n

B\u00e0i 5 (trang 10 SGK Gi\u1ea3i t\u00edch 12):\u00a0Ch\u1ee9ng minh c\u00e1c b\u1ea5t \u0111\u1eb3ng th\u1ee9c sau:<\/strong><\/span><\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a)<\/b>\u00a0X\u00e9t h\u00e0m s\u1ed1 y= f(x) = tanx \u2013 x tr\u00ean kho\u1ea3ng (0; \u03c0\/2)<\/p>\n

Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

=> h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (0; \u03c0\/2)<\/p>\n

Do \u0111\u00f3 v\u1edbi x > 0 => f(x) > f(0) hay tanx – x > 0<\/p>\n

=> tanx > x \u2200 x \u2208 (0; \u03c0\/2) (\u0111pcm)<\/p>\n

b)<\/b>\u00a0X\u00e9t h\u00e0m s\u1ed1<\/p>\n

\"\"<\/p>\n

Theo k\u1ebft qu\u1ea3 c\u00e2u a) th\u00ec tanx > x \u2200 x \u2208 (0; \u03c0\/2)<\/p>\n

Suy ra g'(x) > 0 \u2200 x \u2208 (0; \u03c0\/2)<\/p>\n

=> h\u00e0m s\u1ed1 g'(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (0; \u03c0\/2)<\/p>\n

Do \u0111\u00f3 v\u1edbi x > 0 => g(x) > g(0)<\/p>\n

\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 1 (trang 9 SGK Gi\u1ea3i t\u00edch 12):\u00a0X\u00e9t s\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1: a) y = 4 + 3x \u2013 x2 c) y = x4 – 2×2 + 3 d) y = -x3 + x2 \u2013 5 L\u1eddi gi\u1ea3i: (L\u01b0u \u00fd: \u0110\u1ec3 x\u00e9t xem d\u1ea5u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 + hay – […]<\/p>\n","protected":false},"author":3,"featured_media":21685,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1377,1356,1355],"yoast_head":"\nGi\u1ea3i t\u00edch - Ch\u01b0\u01a1ng 1 - B\u00e0i 1: S\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Gi\u1ea3i t\u00edch - Ch\u01b0\u01a1ng 1 - B\u00e0i 1: S\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 9 SGK Gi\u1ea3i t\u00edch 12):\u00a0X\u00e9t s\u1ef1 \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1: a) y = 4 + 3x \u2013 x2 c) y = x4 – 2×2 + 3 d) y = -x3 + x2 \u2013 5 L\u1eddi gi\u1ea3i: (L\u01b0u \u00fd: \u0110\u1ec3 x\u00e9t xem d\u1ea5u c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 + hay – […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-15T15:34:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-1-trang-9-sgk-giai-tich-12.png\" \/>\n\t<meta property=\"og:image:width\" content=\"577\" \/>\n\t<meta property=\"og:image:height\" content=\"47\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"H\u00e0 Trang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"H\u00e0 Trang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so\/\",\"url\":\"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-1-su-dong-bien-nghich-bien-cua-ham-so\/\",\"name\":\"Gi\u1ea3i t\u00edch - 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