B\u00e0i 62 (trang 57 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1:<\/p>\n

<\/p>\n

b) Ch\u1ee9ng minh r\u1eb1ng giao \u0111i\u1ec3m I c\u1ee7a hai \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u01b0\u1eddng cong \u0111\u00e3 cho l\u00e0 t\u00e2m \u0111\u1ed1i x\u1ee9ng c\u1ee7a n\u00f3.<\/p>\n

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

a) TX\u0110: D = R \\ {-1}<\/p>\n

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

<\/p>\n

H\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean D.<\/p>\n

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

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = -1<\/p>\n

<\/p>\n

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

<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/p>\n

<\/p>\n

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

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

<\/p>\n

Ta c\u00f3 giao \u0111i\u1ec3m c\u1ee7a 2 ti\u1ec7m c\u1eadn I(-1; 1)<\/p>\n

\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ed5i tr\u1ee5c<\/p>\n

<\/p>\n

Thay v\u00e0o h\u00e0m s\u1ed1<\/p>\n

<\/p>\n

=> f(x) l\u00e0 h\u00e0m s\u1ed1 l\u1ebb. v\u1eady f(x) nh\u1eadn I(-1; 1) l\u00e0m t\u00e2m \u0111\u1ed1i x\u1ee9ng.<\/p>\n

B\u00e0i 63 (trang 57 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (H) h\u00e0m s\u1ed1<\/p>\n

<\/p>\n

b)Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng y=mx+m-1 lu\u00f4n \u0111i qua 1 \u0111i\u1ec3m c\u1ed1 \u0111inh c\u1ee7a \u0111\u01b0\u1eddng cong (H) khi m bi\u1ebfn thi\u00ean.<\/p>\n

c) T\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m sao cho \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 cho c\u1eaft \u0111\u01b0\u1eddng cong (H) t\u1ea1i 2 \u0111i\u1ec3m thu\u1ed9c c\u00f9ng m\u1ed9t nh\u00e1nh c\u1ee7a (H).<\/p>\n

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

<\/p>\n

H\u00e0m s\u1ed1 lu\u00f4n ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng<\/p>\n

<\/p>\n

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

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

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x=-1\/2<\/p>\n

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng ngang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y=1\/2<\/p>\n

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

<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1:<\/p>\n

<\/p>\n

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

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

<\/p>\n

b) G\u1ecdi \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh m\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y=mx+m-1 lu\u00f4n \u0111i qua l\u00e0 I.<\/p>\n

<\/p>\n

v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y=mx+m-1<\/p>\n

<\/p>\n

V\u1eady \u0111\u01b0\u1eddng th\u1eb3ng y=mx+m-1 lu\u00f4n \u0111i qua 1 \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh I =(-1; -1) c\u1ee7a \u0111\u01b0\u1eddng cong (H) khi m bi\u1ebfn thi\u00ean.<\/p>\n

B\u00e0i 64 (trang 57 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

Cho h\u00e0m s\u1ed1<\/p>\n

<\/p>\n

a) T\u00ecm a v\u00e0 b bi\u1ebft \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111i qua qua \u0111i\u1ec3m A(-1;5\/2) v\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a (C) t\u1ea1i \u0111i\u1ec3m O(0; 0) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1eb1ng -3.<\/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 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a a v\u00e0 b \u0111\u00e3 t\u00ecm \u0111\u01b0\u1ee3c.<\/p>\n

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

<\/p>\n

G\u1ecdi k l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a ti\u1ebfp tuy\u1ebfn t\u1ea1i \u0111i\u1ec3m O(0; 0) c\u1ee7a \u0111\u1ed3 th\u1ecb (C) ta c\u00f3:<\/p>\n

k=y’ (0)=-3 <=> b=-3 (1)<\/p>\n

M\u1eb7t kh\u00e1c ta c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C) qua \u0111i\u1ec3m A(-1;5\/2)<\/p>\n

<\/p>\n

T\u1eeb (1) th\u1ebf v\u00e0o (2) ta \u0111\u01b0\u1ee3c:<\/p>\n

<\/p>\n

V\u1eady ta c\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a a, b l\u00e0: a = -2; b = -3<\/p>\n

<\/p>\n

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

TX\u0110: D \\ {1}<\/p>\n

<\/p>\n

=> y < 0 \u2200x \u2208 R \\ {1}<\/p>\n

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb c\u00f3 h\u00e0m s\u1ed1 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng: x = 1.<\/p>\n

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn xi\u00ean l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y=-2x+1.<\/p>\n

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

<\/p>\n

<\/p>\n

B\u00e0i 65 (trang 58 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) Kh\u1ea3o s\u00e1t t\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u00ec h\u00e0m s\u1ed1:<\/p>\n

<\/p>\n

b) V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a m \u0111\u01b0\u1eddng th\u1eb3ng y=m-x c\u1eaft \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t?<\/p>\n

c) G\u1ecdi A v\u00e0 B l\u00e0 2 giao \u0111i\u1ec3m \u0111\u00f3. T\u00ecm t\u1eadp h\u1ee3p c\u00e1c trung \u0111i\u1ec3m M c\u1ee7a \u0111o\u1ea1n AB n\u00f3i tr\u00ean m thay \u0111\u1ed5i.<\/p>\n

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

a) TX\u0110: D = R \\ {1}<\/p>\n

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

<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn (-\u221e;0)\u222a(2; +\u221e)<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn (0; 1) \u222a(1;2)<\/p>\n

C\u1ef1c tr\u1ecb: y_{C\u0110<\/sub>=-1 khi x = 0<\/p>\n}

y_{CT<\/sub>=7 khi x = 2<\/p>\n}

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 1<\/p>\n

<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 1 ti\u1ec7m c\u1eadn l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng: y=2x+1<\/p>\n

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

<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/p>\n

<\/p>\n

Ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y=m-x v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nghi\u1ec7m c\u1ee7a Ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

<\/p>\n

<=> (m-x)(x-1)=2x^{2<\/sup>-x+1,x \u2260 1<\/p>\n}

<=> f(x)=3x^{2<\/sup>-x(2+m)+m+1=0,f(1) \u2260 0<\/p>\n}

\u0110\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng (C ) t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t th\u00ec: \u0394>0 v\u00e0 f(1) \u2260 0<\/p>\n

Ta c\u00f3: \u0394=(2+m)^{2<\/sup>-4.3(m+1)>0<\/p>\n}

=m^{2<\/sup>-8m-8>0<\/p>\n}

<\/p>\n

c) G\u1ecdi A(x_{A<\/sub>;yA<\/sub>\u00a0),B(xB<\/sub>,yB<\/sub>) l\u00e0 hai \u0111i\u1ec3m \u0111\u00f3<\/p>\n}

<\/p>\n

g\u1ecdi M(x_{M<\/sub>;yM<\/sub>\u00a0) l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB<\/p>\n}

<\/p>\n

=> y_{M<\/sub>=m-xM<\/sub>=6xM<\/sub>-2-xM<\/sub>=5xM<\/sub>-2<\/p>\n}

V\u1eady t\u1eadp h\u1ee3p trung \u0111i\u1ec3m M c\u1ee7a \u0111o\u1ea1n AB khi m bi\u1ebfn thi\u00ean l\u00e0: y=5x-2<\/p>\n

<\/p>\n

B\u00e0i 66 (trang 58 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

T\u00ecm c\u00e1c h\u1ec7 s\u1ed1 a, b parabol y=2x_{2<\/sub>+ax+b ti\u1ebfp x\u00fac v\u1edbi hypebol y=1\/x t\u1ea1i \u0111i\u1ec3m M(1\/2;2)<\/p>\n}

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

Ti\u1ebfp \u0111i\u1ec3m M ch\u00ednh l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

<\/p>\n

Thay ho\u00e0nh \u0111\u1ed9 c\u1ee7a ti\u1ebfp \u0111i\u1ec3m (M) v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) khi \u0111\u00f3 (I) tr\u1edf th\u00e0nh:<\/p>\n

<\/p>\n

th\u00ec parabol s\u1ebd ti\u1ebfp x\u00fac v\u1edbi hyperbol t\u1ea1i \u0111i\u1ec3m M.<\/p>\n

B\u00e0i 67 (trang 58 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

M\u1ed9t t\u1ea1p ch\u00ed v\u1edbi gi\u00e1 20 ngh\u00ecn \u0111\u1ed3ng mu\u1ed9t cu\u1ed1n. chi ph\u00ed cho xu\u1ea5t b\u1ea3n x cu\u1ed1n t\u1ea1p ch\u1ecb (bao g\u1ed3m: l\u01b0\u01a1ng c\u00e1n b\u1ed9, c\u00f4ng nh\u00e2n vi\u00ean, gi\u1ea5y in, \u2026) \u0111\u01b0\u1ee3c cho b\u1edfi C(x) = 0,0001x^{0<\/sup>-0,2x+10000<\/p>\n}

C(x) \u0111\u01b0\u1ee3c t\u00ednh theo \u0111\u01a1n v\u1ecb v\u1ea1n \u0111\u1ed3ng. Chi ph\u00ed h\u00e0nh cho m\u1ed7i l\u00e0 4 ngh\u00ecn \u0111\u1ed3ng.<\/p>\n

1^{0<\/sup>. a) T\u00ednh t\u1ed5ng chi ph\u00ed T(x) (xu\u1ea5t b\u1ea3n v\u00e0 ph\u00e1t h\u00e0nh) cho x cu\u1ed1n t\u1ea1p ch\u00ed.<\/p>\n}

b) T\u1ec9 s\u1ed1 M(x) = T(x)\/x \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 chi ph\u00ed trung b\u00ecnh cho chi ph\u00ed trung b\u00ecnh l\u00e0 th\u1ea5p nh\u1ea5t.<\/p>\n

2^{0<\/sup>. C\u00e1c kho\u1ea3n thu bao g\u1ed3m ti\u1ec1n s\u00e1ch v\u00e0 90 tri\u1ec7u \u0111\u1ed3ng nh\u1eadn \u0111\u01b0\u1ee3c t\u1eeb qu\u1ea3ng c\u00e1o v\u00e0 s\u1ef1 tr\u1ee3 gi\u00fap c\u1ee7a b\u00e1o ch\u00ed. Gi\u1ea3 s\u1eed s\u1ed1 cu\u1ed1n in ta \u0111\u1ec1u b\u00e1n \u0111\u01b0\u1ee3c h\u1ebft.<\/p>\n}

a) Ch\u1ee9ng minh r\u1eb1ng s\u1ed1 ti\u1ec1n l\u00e3i khi x cu\u1ed1n t\u1ea1p ch\u00ed l\u00e0<\/p>\n

L(x)=-0,0001x^{2<\/sup>+1,8x-1000<\/p>\n}

b) H\u1ecfi in bao nhi\u00eau cu\u1ed1n th\u00ec c\u00f3 l\u00e3i?<\/p>\n

c) In bao nhi\u00eau cu\u1ed1n th\u00ec l\u00e3i nhi\u1ec1u nh\u1ea5t? t\u00ednh s\u1ed1 ti\u1ec1n l\u00e3i \u0111\u00f3.<\/p>\n

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

1^{0<\/sup>. a) Chi ph\u00ed ph\u00e1t h\u00e0nh cho x cu\u1ed1n s\u00e1ch l\u00e0 0,4x (\u0111\u01a1n v\u1ecb v\u1ea1n \u0111\u1ed3ng). V\u1eady t\u1ed5ng chi ph\u00ed T(x) (xu\u1ea5t b\u1ea3n v\u00e0 ph\u00e1t h\u00e0nh) cho x cu\u1ed1n t\u1ea1p ch\u00ed l\u00e0:<\/p>\n}

T(x)=C(x)+0,4x=0,0001x^{2<\/sup>+0,2x+10000<\/p>\n}

b)<\/p>\n

<\/p>\n

\u0110\u1ec3 chi ph\u00ed trung b\u00ecnh l\u00e0 th\u1ea5p nh\u1ea5t th\u00ec c\u1ea7n xu\u1ea5t b\u1ea3n 10000 cu\u1ed1n t\u1ea1p ch\u00ed.<\/p>\n

2^{0<\/sup>. a) S\u1ed1 ti\u1ec1n l\u00e3i khi in x cu\u1ed1n t\u1ea1p ch\u00ed l\u00e0:<\/p>\n}

L(x)=2x+9000-T(x)=2x+9000-(0,0001x^{2<\/sup>+0,2x+10000)<\/p>\n}

=-0,0001x^{2<\/sup>+1,8x-1000<\/p>\n}

b) \u0111\u1ec3 c\u00f3 l\u00e3i th\u00ec L(x) > 0<\/p>\n

<=> -0,0001x^{2<\/sup>+1,8x-1000 > 0<=> 573 < x < 17427<\/p>\n}

c) L(x) = -0, 0002x +1, 8; L’ (x)=0 <=> x=9000<\/p>\n

vh\u00e0m s\u1ed1 L(x) \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i x = 9000<\/p>\n

v\u1eady in 9000 cu\u1ed1n s\u00e1ch th\u00ec l\u00e3i nhi\u1ec1u nh\u1ea5t.<\/p>\n

s\u1ed1 ti\u1ec1n l\u00e3i l\u00e0: L(9000) = 71.000.000 \u0111\u1ed3ng.<\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 62 (trang 57 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1: b) Ch\u1ee9ng minh r\u1eb1ng giao \u0111i\u1ec3m I c\u1ee7a hai \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u01b0\u1eddng cong \u0111\u00e3 cho l\u00e0 t\u00e2m \u0111\u1ed1i x\u1ee9ng c\u1ee7a n\u00f3. L\u1eddi gi\u1ea3i: a) TX\u0110: D = R \\ {-1} S\u1ef1 […]<\/p>\n","protected":false},"author":3,"featured_media":23657,"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