B\u00e0i 1 (trang 211 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng h\u00e0m s\u1ed1 f(x) = e^{2<\/sup>-x-1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean n\u1eeda kho\u1ea3ng [0; +\u221e)<\/p>\n}

b) T\u1eeb \u0111\u00f3 suy ra e^{x<\/sup>>x+1 v\u1edbi m\u1ecdi x > 0<\/p>\n}

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

a) Ta c\u00f3: f\u2019(x) = (e^{x<\/sup>-x-1)’=ex<\/sup>-1<\/p>\n}

f’ (x)\u22650 <=> e^{x<\/sup>-1\u22650 <=> ex<\/sup>\u22651 <=> x \u22650<\/p>\n}

V\u1eady f(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean [0; +\u221e)<\/p>\n

b) V\u00ec f(x) = e^{x<\/sup>-x-1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean [0; +\u221e) n\u00ean:<\/p>\n}

f(x)>f(0)v\u1edbi m\u1ecdi x > 0, m\u00e0 f(0) = 0 n\u00ean ta c\u00f3:<\/p>\n

f(x)>0 <=> e^{x<\/sup>-x-1>0 <=> ex<\/sup>>x+1 (\u0111pcm)<\/p>\n}

B\u00e0i 2 (trang 211 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

a) Kh\u1ea3o s\u00e1t v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f(x) =2x^{3<\/sup>-3x2<\/sup>-12x-10=0<\/p>\n}

b) Ch\u1ee9ng minh r\u1eb1ng Ph\u01b0\u01a1ng tr\u00ecnh 2x^{3<\/sup>-3x2<\/sup>-12x-10=0 c\u00f3 nghi\u1ec7m th\u1ef1c duy nh\u1ea5t.<\/p>\n}

c) G\u1ecdi nghi\u1ec7m duy nh\u1ea5t c\u1ee7a Ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 \u03b1.<\/p>\n

Ch\u1ee9ng minh r\u1eb1ng: 3,5<\u03b1<3,6<\/p>\n

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