B\u00e0i 11 (trang 16 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\nT\u00ecm c\u1ef1c tr\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-529.png\")
<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
a) H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh tr\u00ean R.<\/p>\n
Ta c\u00f3: f\u2019(x) = x2<\/sup>+4x+3<\/p>\nT\u1eeb \u0111\u00f3 f\u2019(x) = 0 <=> x = -1 ho\u1eb7c x = -3<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-362.png\")
<\/p>\n
V\u1eady h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i \u0111i\u1ec3m x = -3, gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 l\u00e0: fC\u0110<\/sub>=f(-3)=-1.<\/p>\nH\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i \u0111i\u1ec3m x = -1, gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3n c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 fCT<\/sub>=f(-1)=-7\/3<\/p>\nb) T\u1eadp x\u00e1c \u0111\u1ecbnh: R<\/p>\n
f’ (x)=x2<\/sup>-2x+2=(x-1)2<\/sup>+1>0,\u2200x \u2208R=>f(x) lu\u00f4n \u0111\u1ed3ng bi\u1ebfn n\u00ean h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\nc) T\u1eadp x\u00e1c \u0111\u1ecbnh: R \\ {0}<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-197.png\")
<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/4-119.png\")
<\/p>\n
V\u1eady h\u00e0m s\u1ed1 c\u1ef1c \u0111\u1ea1i t\u1ea1i x = -1; fC\u0110<\/sub>=f(-1)=-2<\/p>\nH\u00e0m s\u1ed1 c\u1ef1c ti\u1ec3u t\u1ea1i x = 1; fCT<\/sub>=f(1)=2<\/p>\nd) f(x) x\u00e1c \u0111\u1ecbnh li\u00ean t\u1ee5c tr\u00ean R.<\/p>\n
ta c\u00f3:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/5-88.png\")
<\/p>\n
b\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/6-54.png\")
<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = -1, fC\u0110<\/sub>=f(-1)=1<\/p>\nH\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0, fCT<\/sub>=f(0)=1<\/p>\ne) t\u1eadp x\u00e1c \u0111\u1ecbnh: R<\/p>\n
f\u2019(x) = x4<\/sup>-x2<\/sup>;f’ (x)=0 <=> x = 0 ho\u1eb7c x=\u00b11<\/p>\nb\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/7-41.png\")
<\/p>\n
V\u1eady h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = -1, fC\u0110<\/sub>=f(-1)=32\/15<\/p>\nH\u00e0m s\u1ed1 c\u1ef1c ti\u1ec3u t\u1ea1i x = 1; fCT<\/sub>=f(1)=28\/15<\/p>\nf) T\u1eadp x\u00e1c \u0111\u1ecbnh: R \\ {1}<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/8-28.png\")
<\/p>\n
f’ (x)=0 <=> x = 0 ho\u1eb7c x = 2<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/9-19.png\")
<\/p>\n
B\u00e0i 12 (trang 17 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\nT\u00ecm c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 sau:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-530.png\")
<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
a) T\u1eadp x\u00e1c \u0111\u1ecbnh: [-2; 2]<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-363.png\")
<\/p>\n
y’=0 <=> x=\u00b1\u221a2<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-198.png\")
<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x=-\u221a2,yCT<\/sub>=y(-\u221a2 )=-2<\/p>\nH\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = \u221a2,yC\u0110<\/sub>=y(\u221a2)=2<\/p>\nb) T\u1eadp x\u00e1c \u0111\u1ecbnh: [-2\u221a2;2\u221a2]<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/4-120.png\")
<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/5-89.png\")
<\/p>\n
H\u00e0m s\u1ed1 c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 0; yC\u0110<\/sub>=y(0)=2\u221a2<\/p>\nH\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c ti\u1ec3u.<\/p>\n
c) T\u1eadp x\u00e1c \u0111\u1ecbnh: R<\/p>\n
y’=(x-sin\u20612x+2)’=1-2 cos\u20612x<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/6-55.png\")
<\/p>\n
V\u1eady h\u00e0m s\u1ed1 c\u1ef1c \u0111\u1ea1i t\u1ea1i \u0111i\u1ec3m<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/7-42.png\")
<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i ti\u1ec3u<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/8-29.png\")
<\/p>\n
d) T\u1eadp x\u00e1c \u0111\u1ecbnh: R<\/p>\n
y’=2 sin\u2061x+2.sin\u20612x=2 sin\u2061x(1+2 cos\u2061x )<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/9-20.png\")
<\/p>\n
=> y” (k \u03c0)>0 (c\u00f3 th\u1ec3 vi\u1ebft: y” (k \u03c0)=4+2 cos\u2061(k \u03c0)<\/p>\n
N\u00ean h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i c\u00e1c \u0111i\u1ec3m<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/10-11.png\")
<\/p>\n
n\u00ean h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i c\u00e1c \u0111i\u1ec3m.<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/11-9.png\")
<\/p>\n
B\u00e0i 13 (trang 17 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\nT\u00ecm c\u00e1c h\u1ec7 s\u1ed1 a, b, c, d c\u1ee7a h\u00e0m s\u1ed1 f(x) = ax^3+bx^2+cx+d sao cho h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i \u0111i\u1ec3m x = 0; f(0) = 0 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i \u0111i\u1ec3m x = 1, f(1) = 1<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
Ta c\u00f3 f\u2019(x) = 3ax2<\/sup>+2bx+c=>f’ (0)=c;f’ (1)=3a+2b+c<\/p>\nV\u00ec f(0) = 0 =>d= 0<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = 0 n\u00ean f\u2019(0) = 0 => c =0; f(1) = a + b = 1<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i \u0111i\u1ec3m x = 1 n\u00ean f\u2019(1) = 0 => 3a + 2b = 0<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-531.png\")
<\/p>\n
ta \u0111\u01b0\u1ee3c a = -2; b = 3<\/p>\n
V\u1eadt f(x) = -2x2<\/sup>+3x2<\/sup><\/p>\nTh\u1eed l\u1ea1i f\u2019(x) = -6x2<\/sup>+6x;f” (x)=-12x+6<\/p>\nf\u2019\u2019(0) > 0. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i \u0111i\u1ec3m x = 0<\/p>\n
f\u2019\u2019(1) = -6 < 0. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = 1<\/p>\n
\u0110\u00e1p s\u1ed1: a = -2; b = 3; c =3; d = 0<\/p>\n
\n
\n
B\u00e0i 14 (trang 17 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\nX\u00e1c \u0111\u1ecbnh c\u00e1c h\u1ec7 s\u1ed1 a, b, c sao cho h\u00e0m s\u1ed1: (x) = x3<\/sub>+ax2<\/sub>+bc+c \u0111\u1ea1t c\u1ef1c tr\u1ecb b\u1eb1ng 0 t\u1ea1i x = -2 v\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111i qua A(1; 0)<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
f'(x) = 3x2<\/sup>+2ax+b<\/p>\n\u0110i\u1ec1n ki\u1ec7n c\u1ea7n:<\/p>\n
H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c tr\u1ecb b\u1eb1ng 0 t\u1ea1i x = -2 => f\u2019(2) = 0 v\u00e0 f(-2) = 0<\/p>\n
Hay -4a+b+12=0 (1)v\u00e0 4a-2b+c-8=0 (2)<\/p>\n
\u0110\u1ed3 th\u1ecb \u0111i qua A(1; 0) => a+b+c+1=0<\/p>\n
Gi\u1ea3i h\u1ec7 Ph\u01b0\u01a1ng tr\u00ecnh (1), (2), (3) ta \u0111\u01b0\u1ee3c a =3; b = 0; c = -2<\/p>\n
\u0110i\u1ec1u ki\u1ec7n \u0111\u1ee7:<\/p>\n
X\u00e9t f(x) = x3<\/sup>+3x2<\/sup>-4. Ta c\u00f3: \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f(x) \u0111i qua A(1; 0)<\/p>\nf\u2019(x) = 3x3<\/sup>+6x=>f” (x)=6x+6<\/p>\nf\u2019(-2)= 0; f\u2019\u2019(2) = -6 < 0 n\u00ean x = -2 l\u00e0 \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i v\u00e0 f(-2) = 0<\/p>\n
\u0110\u00e1p s\u1ed1:a =3; b =0; c = -4<\/p>\n
\n
\n
B\u00e0i 15 (trang 17 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\nCh\u1ee9ng minh r\u1eb1ng v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a m, n h\u00e0m s\u1ed1 lu\u00f4n c\u00f3 c\u1ef1c \u0111\u1ea1i v\u00e0 c\u1ef1c ti\u1ec3u..<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
H\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c vi\u1ebft l\u1ea1i l\u00e0:<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-532.png\")
<\/p>\n
H\u00e0m s\u1ed1 x\u00e1c \u0111\u1ecbnh \u2200x \u2260 m<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-364.png\")
<\/p>\n
B\u1ea3ng bi\u1ebfn thi\u00ean<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-199.png\")
<\/p>\n
V\u1eady v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a m, h\u00e0m s\u1ed1 \u0111\u1ea1t \u0111\u01b0\u1ee3c c\u1ef1c \u0111\u1ea1i t\u1ea1i x = m -1 v\u00e0 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = m + 1<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
B\u00e0i 11 (trang 16 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):\u00a0 T\u00ecm c\u1ef1c tr\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau: L\u1eddi gi\u1ea3i: a) H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh tr\u00ean R. Ta c\u00f3: f\u2019(x) = x2+4x+3 T\u1eeb \u0111\u00f3 f\u2019(x) = 0 <=> x = -1 ho\u1eb7c x = -3 B\u1ea3ng bi\u1ebfn thi\u00ean V\u1eady h\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c […]<\/p>\n","protected":false},"author":3,"featured_media":23965,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n
\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: C\u1ef1c tr\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\/dai-so-chuong-1-bai-2-cuc-tri-cua-ham-so\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: C\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 11 (trang 16 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):\u00a0 T\u00ecm c\u1ef1c tr\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau: L\u1eddi gi\u1ea3i: a) H\u00e0m s\u1ed1 \u0111\u00e3 cho x\u00e1c \u0111\u1ecbnh tr\u00ean R. 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