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{"id":21259,"date":"2018-03-15T00:15:13","date_gmt":"2018-03-14T17:15:13","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=21259"},"modified":"2018-03-15T00:15:13","modified_gmt":"2018-03-14T17:15:13","slug":"giai-tich-chuong-1-bai-5-khao-sat-su-bien-thien-va-ve-thi-cua-ham","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/giai-tich-chuong-1-bai-5-khao-sat-su-bien-thien-va-ve-thi-cua-ham\/","title":{"rendered":"Gi\u1ea3i t\u00edch – Ch\u01b0\u01a1ng 1 – B\u00e0i 5: Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1"},"content":{"rendered":"

B\u00e0i 1 (trang 43 SGK Gi\u1ea3i t\u00edch 12):\u00a0Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 b\u1eadc ba sau:<\/strong><\/span><\/p>\n

\n

a) y = 2 + 3x – x3<\/sup>\u00a0; \u00a0\u00a0\u00a0 b) y = x3<\/sup>\u00a0+ 4x2<\/sup>\u00a0+ 4x<\/p>\n

c) y = x3<\/sup>\u00a0+ x2<\/sup>\u00a0+ 9x ; \u00a0\u00a0\u00a0 d) y = -2x3<\/sup>\u00a0+ 5<\/p>\n

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

a)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 3 – 3x2<\/sup><\/p>\n

y’ = 0 => x = \u00b11<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (1; 1 ).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; -1) v\u00e0 (1; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0: ( 1; 0).<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (1; 4).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

Ta c\u00f3 x3<\/sup>\u00a0+ 4x2<\/sup>\u00a0+ 4x = 0 \u21d2 x(x2<\/sup>\u00a0+ 4x + 4) = 0<\/p>\n

\u21d2 x(x + 2)2<\/sup>\u00a0= 0 => x = 0; x = -2<\/p>\n

+ Giao v\u1edbi Ox: (0; 0) v\u00e0 (-2; 0)<\/p>\n

+ Giao v\u1edbi Oy: (0; 0) (v\u00ec y(0) = 0)<\/p>\n

\"\"<\/p>\n

(\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nh\u1eadn \u0111i\u1ec3m (0; 2) l\u00e0m t\u00e2m \u0111\u1ed1i x\u1ee9ng.)<\/p>\n

\n

b)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 3x2<\/sup>\u00a0+ 8x + 4<\/p>\n

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

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

Ta c\u00f3 2 + 3x – x3<\/sup>\u00a0= 0 \u21d2 x = -1 ; x = 2<\/p>\n

+ Giao v\u1edbi Ox: (-1; 0) v\u00e0 (2; 0)<\/p>\n

+ Giao v\u1edbi Oy: (0; 2) (v\u00ec y(0) = 2)<\/p>\n

\"\"<\/p>\n

c)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 3x2<\/sup>\u00a0+ 2x + 9 > 0 \u2200 x \u2208 R<\/p>\n

=> H\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean R v\u00e0 kh\u00f4ng c\u00f3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n\n\n\n\n
x<\/td>\n0<\/td>\n1<\/td>\n-1<\/td>\n<\/tr>\n
y<\/td>\n0<\/td>\n11<\/td>\n-9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\"\"<\/p>\n

d)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = -6x2<\/sup>\u00a0\u2264 0 \u2200 x \u2208 R<\/p>\n

=> H\u00e0m s\u1ed1 lu\u00f4n ngh\u1ecbch bi\u1ebfn tr\u00ean R v\u00e0 kh\u00f4ng c\u00f3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n\n\n\n\n
x<\/td>\n0<\/td>\n1<\/td>\n-1<\/td>\n<\/tr>\n
y<\/td>\n5<\/td>\n3<\/td>\n7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\"\"<\/p>\n

B\u00e0i 2 (trang 43 SGK Gi\u1ea3i t\u00edch 12):\u00a0Kh\u1ea3o s\u00e1t t\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n sau:<\/strong><\/span><\/p>\n

a) y = -x4<\/sup>\u00a0+ 8x2<\/sup>\u00a0– 1 ; \u00a0\u00a0\u00a0 b) y = x4<\/sup>\u00a0– 2x2<\/sup>\u00a0+ 2<\/p>\n

\"\"<\/p>\n

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

a)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = -4x3<\/sup>\u00a0+ 16x = -4x(x2<\/sup>\u00a0– 4)<\/p>\n

y’ = 0 \u21d4 -4x(x2<\/sup>\u00a0– 4) = 0 => x = 0 ; x = \u00b12<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; -2) v\u00e0 (0; 2).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-2; 0) v\u00e0 (2; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0: (0; -1).<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (-2; 15) v\u00e0 (2; 15).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

H\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 h\u00e0m s\u1ed1 ch\u1eb5n, v\u00ec:<\/p>\n

y(-x) = -(-x)4<\/sup>\u00a0+ 8(-x)2<\/sup>\u00a0– 1 = -x4<\/sup>\u00a0+ 8x2<\/sup>\u00a0– 1 = y(x)<\/p>\n

Do \u0111\u00f3 \u0111\u1ed3 th\u1ecb nh\u1eadn Oy l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng.<\/p>\n

Ta c\u00f3: -x4<\/sup>\u00a0+ 8x2<\/sup>\u00a0– 1 = 0 => x = \u00b1\u221a(4 + \u221a15) ; x = \u00b1\u221a(4 – \u221a15)<\/p>\n

+ Giao v\u1edbi Ox: t\u1ea1i 4 \u0111i\u1ec3m<\/p>\n

+ Giao v\u1edbi Oy: (0; -1) (v\u00ec y(0) = -1)<\/p>\n

\"\"<\/p>\n

b)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 4x3<\/sup>\u00a0– 4x = 4x(x2<\/sup>\u00a0– 1)<\/p>\n

y’ = 0 \u21d4 4x(x2<\/sup>\u00a0– 1) = 0 => x = 0 ; x = \u00b11<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-1; 0) v\u00e0 (1; +\u221e).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; -1) v\u00e0 (0; 1).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0: (-1; 1) v\u00e0 (1; 1).<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (0; 2).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

X\u00e1c \u0111\u1ecbnh t\u01b0\u01a1ng t\u1ef1 nh\u01b0 a) ta c\u00f3 \u0111\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

c)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 2x3<\/sup>\u00a0+ 2x = 2x(x2<\/sup>\u00a0+ 1)<\/p>\n

y’ = 0 \u21d4 2x(x2<\/sup>\u00a0+ 1) = 0 => x = 0<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (0; +\u221e).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; 0).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (0; -3\/2).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

X\u00e1c \u0111\u1ecbnh t\u01b0\u01a1ng t\u1ef1 nh\u01b0 a) ta c\u00f3 \u0111\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

d)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = -4x – 4x3<\/sup>\u00a0= -4x(1 + x2<\/sup>)<\/p>\n

y’ = 0 \u21d4 -4x(1 + x2<\/sup>) = 0 => x = 0<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-\u221e; 0).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (0; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (0; 3).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

X\u00e1c \u0111\u1ecbnh t\u01b0\u01a1ng t\u1ef1 nh\u01b0 a) ta c\u00f3 \u0111\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

B\u00e0i 3 (trang 43 SGK Gi\u1ea3i t\u00edch 12):\u00a0Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u00e1c h\u00e0m s\u1ed1 ph\u00e2n th\u1ee9c:<\/strong><\/span><\/p>\n

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

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

\n

a)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R \\ {1}<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean:<\/p>\n

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

=> H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean (-\u221e; 1) v\u00e0 (1; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb: H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

+ Ti\u1ec7m c\u1eadn:<\/p>\n

\"\"<\/p>\n

V\u1eady x = 1 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>\n

\"\"<\/p>\n

V\u1eady y = 1 l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

+ Giao v\u1edbi Oy: (0; -3)<\/p>\n

+ Giao v\u1edbi Ox: (-3; 0)<\/p>\n

\"\"<\/p>\n

b)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R \\ {2}<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

=> H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean (-\u221e; 2) v\u00e0 (2; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb: H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

+ Ti\u1ec7m c\u1eadn:<\/p>\n

\"\"<\/p>\n

V\u1eady x = 2 l\u00e0 ti\u1ec7m c\u1ea1n \u0111\u1ee9ng.<\/p>\n

\"\"<\/p>\n

V\u1eady y = -1 l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

+ Giao v\u1edbi Oy: (0; -1\/4)<\/p>\n

+ Giao v\u1edbi Ox: (1\/2; 0)<\/p>\n

X\u00e1c \u0111\u1ecbnh m\u1ed9t s\u1ed1 \u0111i\u1ec3m kh\u00e1c:<\/p>\n

\"\"<\/p>\n

c)<\/b><\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R \\ {-1\/2}<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

=> H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean (-\u221e; -1\/2) v\u00e0 (-1\/2; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb: H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

+ Ti\u1ec7m c\u1eadn:<\/p>\n

\"\"<\/p>\n

V\u1eady x = -1\/2 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>\n

\"\"<\/p>\n

V\u1eady y = -1\/2 l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

+ Giao v\u1edbi Oy: (0; 2)<\/p>\n

+ Giao v\u1edbi Ox: (2; 0)<\/p>\n

\"\"<\/p>\n

B\u00e0i 4 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0B\u1eb1ng c\u00e1ch kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1, h\u00e3y t\u00ecm s\u1ed1 nghi\u1ec7m c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh sau:<\/strong><\/span><\/p>\n

a) x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5 = 0 ;<\/strong><\/span><\/p>\n

b) -2x3<\/sup>\u00a0+ 3x2<\/sup>\u00a0– 2 = 0 ;<\/strong><\/span><\/p>\n

c) 2x2<\/sup>\u00a0– x4<\/sup>\u00a0= -1<\/strong><\/span><\/p>\n

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

a)<\/b>\u00a0x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5 = 0 \u00a0\u00a0\u00a0 (1)<\/p>\n

S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (1) l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5 v\u00e0 tr\u1ee5c ho\u00e0nh (y = 0).<\/p>\n

X\u00e9t h\u00e0m s\u1ed1 y = x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5 ta c\u00f3:<\/p>\n

– TX\u0110: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 3x2<\/sup>\u00a0– 6x = 3x(x – 2)<\/p>\n

y’ = 0 => x = 0 ; x = 2<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

\u00a0\u00a0\u00a0 + B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

+ \u0110\u1ed3 th\u1ecb<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5\u00a0ch\u1ec9 c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i 1 \u0111i\u1ec3m duy nh\u1ea5t<\/b>. T\u1eeb \u0111\u00f3 suy ra ph\u01b0\u01a1ng tr\u00ecnh x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 5 = 0 ch\u1ec9 c\u00f3 1 nghi\u1ec7m.<\/p>\n

b)<\/b>\u00a0-2x3<\/sup>\u00a0+ 3x2<\/sup>\u00a0– 2 = 0<\/p>\n

\u21d4 2x3<\/sup>\u00a0– 3x2<\/sup>\u00a0= -2 \u00a0\u00a0\u00a0 (2)<\/p>\n

S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (2) l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x3<\/sup>\u00a0– 3x2<\/sup>\u00a0v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = -2.<\/p>\n

X\u00e9t h\u00e0m s\u1ed1 y = 2x3<\/sup>\u00a0– 3x2<\/sup><\/p>\n

– TX\u0110: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 6x2<\/sup>\u00a0– 6x = 6x(x – 1)<\/p>\n

y’ = 0 => x = 0 ; x = 1<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

\u00a0\u00a0\u00a0 + B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

\n<\/div>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x3<\/sup>\u00a0– 3x2<\/sup>ch\u1ec9 c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng y = -2 t\u1ea1i 1 \u0111i\u1ec3m duy nh\u1ea5t<\/b>. T\u1eeb \u0111\u00f3 suy ra ph\u01b0\u01a1ng tr\u00ecnh 2x3<\/sup>\u00a0– 3x2<\/sup>\u00a0= -2 ch\u1ec9 c\u00f3 1 nghi\u1ec7m.<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh -2x3<\/sup>\u00a0+ 3x2<\/sup>\u00a0– 2 = 0 ch\u1ec9 c\u00f3 m\u1ed9t nghi\u1ec7m.<\/p>\n

c)<\/b>\u00a02x2<\/sup>\u00a0– x4<\/sup>\u00a0= -1 \u00a0\u00a0\u00a0 (3)<\/p>\n

S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (3) l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x2<\/sup>\u00a0– x4<\/sup>\u00a0v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = -1.<\/p>\n

X\u00e9t h\u00e0m s\u1ed1 y = 2x2<\/sup>\u00a0– x4<\/sup>\u00a0ta c\u00f3:<\/p>\n

– TX\u0110: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = 4x – 4x3<\/sup>\u00a0= 4x(1 – x2<\/sup>)<\/p>\n

y’ = 0 => x = 0 ; x = \u00b11<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x2<\/sup>\u00a0– x4<\/sup>c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng y = -1 t\u1ea1i hai \u0111i\u1ec3m<\/b>. T\u1eeb \u0111\u00f3 suy ra ph\u01b0\u01a1ng tr\u00ecnh 2x2<\/sup>\u00a0– x4<\/sup>\u00a0= -1 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t.<\/p>\n

B\u00e0i 5 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1:<\/strong><\/span><\/p>\n

y = -x3<\/sup>\u00a0+ 3x + 1<\/strong><\/span><\/p>\n

b) D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb (C), bi\u1ec7n lu\u1eadn v\u1ec1 s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh sau theo tham s\u1ed1 m:<\/strong><\/span><\/p>\n

x3<\/sup>\u00a0– 3x + m = 0<\/strong><\/span><\/p>\n

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

a)<\/b>\u00a0Kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 y = -x3<\/sup>\u00a0+ 3x + 1<\/p>\n

– T\u1eadp x\u00e1c \u0111\u1ecbnh: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = -3x2<\/sup>\u00a0+ 3 = -3(x2<\/sup>\u00a0– 1)<\/p>\n

y’ = 0 \u21d4 -3(x2<\/sup>\u00a0– 1) = 0 \u21d4 x = \u00b11<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng (-1; 1).<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; -1) v\u00e0 (1; +\u221e).<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0: (-1; -1).<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0: (1; 3).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

+ Giao v\u1edbi Oy: (0; 1).<\/p>\n

+ \u0110\u1ed3 th\u1ecb (C) \u0111i qua \u0111i\u1ec3m (-2; 3), (2;-1).<\/p>\n

\"\"<\/p>\n

b)<\/b>\u00a0Ta c\u00f3: x3<\/sup>\u00a0– 3x + m = 0 (*) \u21d4 -x3<\/sup>\u00a0+ 3x = m<\/p>\n

\u21d4 -x3<\/sup>\u00a0+ 3x + 1 = m + 1<\/p>\n

S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (*) ch\u00ednh b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C) v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng (d): y = m + 1.<\/p>\n

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

Bi\u1ec7n lu\u1eadn:<\/b>\u00a0T\u1eeb \u0111\u1ed3 th\u1ecb ta c\u00f3:<\/p>\n

+ N\u1ebfu m + 1 < \u20131 \u21d4 m < \u20132 th\u00ec (C ) c\u1eaft (d) t\u1ea1i 1 \u0111i\u1ec3m.<\/p>\n

+ N\u1ebfu m + 1 = \u20131 \u21d4 m = \u20132 th\u00ec (C ) c\u1eaft (d) t\u1ea1i 2 \u0111i\u1ec3m.<\/p>\n

+ N\u1ebfu \u20131 < m + 1 < 3 \u21d4 \u20132 < m < 2 th\u00ec (C ) c\u1eaft (d) t\u1ea1i 3 \u0111i\u1ec3m.<\/p>\n

+ N\u1ebfu m + 1 = 3 \u21d4 m = 2 th\u00ec (C ) c\u1eaft (d) t\u1ea1i 2 \u0111i\u1ec3m.<\/p>\n

+ N\u1ebfu m + 1 > 3 \u21d4 m > 2 th\u00ec (C ) c\u1eaft (d) t\u1ea1i 1 \u0111i\u1ec3m.<\/p>\n

T\u1eeb \u0111\u00f3 suy ra s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh x3<\/sup>\u00a0– 3x + m = 0 ph\u1ee5 thu\u1ed9c tham s\u1ed1 m nh\u01b0 sau:<\/p>\n

+ Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 1 nghi\u1ec7m n\u1ebfu m < -2 ho\u1eb7c m > 2.<\/p>\n

+ Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m n\u1ebfu m = -2 ho\u1eb7c m = 2.<\/p>\n

+ Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 3 nghi\u1ec7m n\u1ebfu: -2 < m < 2.<\/p>\n

B\u00e0i 6 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

\"\"<\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1 m, h\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng x\u00e1c \u0111\u1ecbnh c\u1ee7a n\u00f3.<\/p>\n

b) X\u00e1c \u0111\u1ecbnh m \u0111\u1ec3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb \u0111i qua A(-1, \u221a2).<\/p>\n

c) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 khi m = 2.<\/p>\n

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

a)<\/b>\u00a0Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

V\u1eady h\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean m\u1ed7i kho\u1ea3ng x\u00e1c \u0111\u1ecbnh c\u1ee7a n\u00f3.<\/p>\n

b)<\/b>\u00a0Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

V\u1eady v\u1edbi m = 2 th\u00ec ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb \u0111i qua A(-1, \u221a2)<\/p>\n

\n

c)<\/b>\u00a0V\u1edbi m = 2 ta \u0111\u01b0\u1ee3c h\u00e0m s\u1ed1:<\/p>\n

\"\"<\/p>\n

X\u00e9t h\u00e0m s\u1ed1 tr\u00ean ta c\u00f3:<\/p>\n

– TX\u0110: D = R \\ {-1}<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

=> H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean D.<\/p>\n

+ Ti\u1ec7m c\u1eadn:<\/p>\n

\"\"<\/p>\n

=> \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = -1.<\/p>\n

\"\"<\/p>\n

=> \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 y = 1.<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

M\u1ed9t s\u1ed1 \u0111i\u1ec3m thu\u1ed9c \u0111\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

B\u00e0i 7 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

\"\"<\/p>\n

a) V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a tham s\u1ed1 m, \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m \u0111i qua \u0111i\u1ec3m (-1; 1) ?<\/p>\n

b) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 khi m = 1.<\/p>\n

c) Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn (C) t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng 7\/4.<\/p>\n

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

a)<\/b>\u00a0\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 qua \u0111i\u1ec3m (-1; 1) khi v\u00e0 ch\u1ec9 khi:<\/p>\n

\"\"<\/p>\n

b)<\/b>\u00a0V\u1edbi m = 1, ta c\u00f3:<\/p>\n

\"\"<\/p>\n

– TX\u0110: D = R<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean: y’ = x3<\/sup>\u00a0+ x = x(x2<\/sup>\u00a0+ 1)<\/p>\n

y’ = 0 \u21d4 x(x2<\/sup>\u00a0+ 1) \u21d4 x = 0<\/p>\n

+ Gi\u1edbi h\u1ea1n:<\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean (0; +\u221e) v\u00e0 ngh\u1ecbch bi\u1ebfn tr\u00ean (-\u221e; 0)<\/p>\n

+ C\u1ef1c tr\u1ecb:<\/p>\n

H\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c ti\u1ec3u l\u00e0 (0; 1).<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

\"\"<\/p>\n

c) \u0110i\u1ec3m thu\u1ed9c (C) c\u00f3 tung \u0111\u1ed9 b\u1eb1ng 7\/4 n\u00ean ho\u00e0nh \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m \u0111\u00f3 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

\"\"<\/p>\n

B\u00e0i 8 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1:<\/strong><\/span><\/p>\n

y = x3<\/sup>\u00a0+ (m + 3)x2<\/sup>\u00a0+ 1 – m (m l\u00e0 tham s\u1ed1) c\u00f3 \u0111\u1ed3 th\u1ecb (Cm<\/sub>).<\/strong><\/span><\/p>\n

a) X\u00e1c \u0111\u1ecbnh m \u0111\u1ec3 h\u00e0m s\u1ed1 c\u00f3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0 x = -1.<\/strong><\/span><\/p>\n

b) X\u00e1c \u0111\u1ecbnh m \u0111\u1ec3 \u0111\u1ed3 th\u1ecb (Cm<\/sub>) c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i x = -2.<\/strong><\/span><\/p>\n

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

a)<\/b>\u00a0Ta c\u00f3: y’ = 3x2<\/sup>\u00a0+ 2(m + 3)x = x[3x + 2(m + 3)]<\/p>\n

y’ = 0 \u21d4 x[3x + 2(m + 3)] = 0 \u21d4 x1<\/sub>\u00a0= 0; x2<\/sub>\u00a0= [-2(m + 3)]\/3 = -2\/3 m – 2<\/p>\n

– N\u1ebfu x1<\/sub>\u00a0= x2<\/sub>\u00a0=> -2\/3 m – 2 = 0 => m = -3<\/p>\n

Khi \u0111\u00f3 y’ = 3x2<\/sup>\u00a0\u2265 0 hay h\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean R n\u00ean kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb (lo\u1ea1i).<\/p>\n

Do \u0111\u00f3 \u0111\u1ec3 h\u00e0m s\u1ed1 c\u00f3 c\u1ef1c tr\u1ecb th\u00ec m \u2260 -3.<\/p>\n

– N\u1ebfu x1<\/sub>\u00a0< x2<\/sub>\u00a0\u21d4 m = -3 ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

Lo\u1ea1i v\u00ec d\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0 x = 0.<\/p>\n

– N\u1ebfu x1<\/sub>\u00a0> x2<\/sub>\u00a0\u21d4 m < -3 ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0 x = -2\/3 m – 2.<\/p>\n

\u0110\u1ec3 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i l\u00e0 x = -1 th\u00ec:<\/p>\n

\"\"<\/p>\n

 <\/p>\n

b)<\/b>\u00a0\u0110\u1ed3 th\u1ecb (Cm<\/sub>) c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i x = -2 suy ra:<\/p>\n

(-2)3<\/sup>\u00a0+ (m + 3)(-2)2<\/sup>\u00a0+ 1 – m = 0 (*)<\/p>\n

=> -8 + 4(m + 3) + 1 – m = 0<\/p>\n

=> 3m + 5 = 0 =>\u00a0m = -5\/3<\/b><\/p>\n

(Gi\u1ea3i th\u00edch *<\/b>: C\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i x = -2 n\u00ean t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m l\u00e0 (-2; 0). Thay t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c (*).)<\/p>\n

B\u00e0i 9 (trang 44 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

\"\"<\/p>\n

c\u00f3 \u0111\u1ed3 th\u1ecb (G).<\/p>\n

a) X\u00e1c \u0111\u1ecbnh m \u0111\u1ec3 \u0111\u1ed3 th\u1ecb (G) \u0111i qua \u0111i\u1ec3m (0; -1).<\/p>\n

b) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 v\u1edbi m t\u00ecm \u0111\u01b0\u1ee3c.<\/p>\n

c) Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb tr\u00ean t\u1ea1i giao \u0111i\u1ec3m c\u1ee7a n\u00f3 v\u1edbi tr\u1ee5c tung.<\/p>\n

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

a)<\/b>\u00a0\u0110\u1ed3 th\u1ecb (G) \u0111i qua \u0111i\u1ec3m (0; -1) khi v\u00e0 ch\u1ec9 khi:<\/p>\n

\"\"<\/p>\n

b)<\/b>\u00a0V\u1edbi m = 0 ta \u0111\u01b0\u1ee3c h\u00e0m s\u1ed1:<\/p>\n

\"\"<\/p>\n

\u00a0TX\u0110: D = R \\ {1}<\/p>\n

– S\u1ef1 bi\u1ebfn thi\u00ean:<\/p>\n

+ Chi\u1ec1u bi\u1ebfn thi\u00ean:<\/p>\n

\"\"<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean D.<\/p>\n

+ Ti\u1ec7m c\u1eadn:<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = 1.<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 y = 1.<\/p>\n

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

\"\"<\/p>\n

– \u0110\u1ed3 th\u1ecb:<\/p>\n

+ Giao \u0111i\u1ec3m v\u1edbi Ox: (-1; 0)<\/p>\n

+ Giao \u0111i\u1ec3m v\u1edbi Oy: (0; -1)<\/p>\n

\"\"<\/p>\n

c)<\/b>\u00a0\u0110\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m P(0;-1), khi \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn t\u1ea1i \u0111i\u1ec3m P(0; -1) l\u00e0:<\/p>\n

y = y'(0).(x – 0) – 1 => y = -2x – 1<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ea7n t\u00ecm l\u00e0: y = -2x – 1<\/p>\n<\/div>\n

\n

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

B\u00e0i 1 (trang 43 SGK Gi\u1ea3i t\u00edch 12):\u00a0Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 b\u1eadc ba sau: a) y = 2 + 3x – x3\u00a0; \u00a0\u00a0\u00a0 b) y = x3\u00a0+ 4×2\u00a0+ 4x c) y = x3\u00a0+ x2\u00a0+ 9x ; \u00a0\u00a0\u00a0 d) y = -2×3\u00a0+ 5 L\u1eddi gi\u1ea3i: a) – […]<\/p>\n","protected":false},"author":3,"featured_media":21262,"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 5: Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb 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-5-khao-sat-su-bien-thien-va-ve-thi-cua-ham\/\" \/>\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 5: Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 43 SGK Gi\u1ea3i t\u00edch 12):\u00a0Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 b\u1eadc ba sau: a) y = 2 + 3x – x3\u00a0; 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