Відповіді АЛГЕБРА: 22.11 (1-2)

22.11

1) f(x) = 3x+1x-1

f’(x) = 3x-1- (3x+1)(x-1)2 = 3x-3-3x-1(x-1)2 = –4(x-1)2

f’(x) = 0;

∅ нема точок екстремуму.

2) g(x) = x9 + 9x

g’(x) = 19 – 9x2

19 – 9x2

x2- 819x2 = 0;

x ≠ 0;

x = ± 9;

gmax (–9) = –99 + 9-9 = –2;

gmin (9) = 99 + 99 = 2.

3) t(x) = 2xx2+ 1

t’(x) = 2x2+1- 2x • 2x(x2+ 1)2 = 2x2+ 2-4x2(x2+ 1)2 = 2-2x2(x2+ 1)2

2-2x2(x2+ 1)2 = 0;

x = ± 1;

tmin (–1) = -21+1 = –22 = –1;

tmax (1) = 22 = 1.

4) φ(x) = 4x – x; D(y): x ≥ 0;

φ’(x) = 42x – 1 = 2x – 1;

φ’(x) = 0;

x = 2;

x = 4;

Xmax = 4;

φmax (4) = 4 • 4 – 4 = 8 – 4 = 4.