Відповіді АЛГЕБРА: 22.14 (1)

22.14

1) φ(x) = x²(x + 2)²

φ’(x) = 2x(x + 2)² + x² • 2(x + 2) = 2x(x + 2)(x + 2 + x) = 2x(x +

+ 2)(2x + 2);

φ’(x) = 0;

x = 0; x = –2; x = –1;

Xmin = –2 ; Xmin = 0; φmin = 0;

Xmax = –1; φmax = (–1)² • (–1 + 2)² = 1 • 1 = 1.

2) g(x) = 1x2+ 6x+8

D(y): x ≠ = –4;

x ≠ –2;

g’(x) = –2x+6(x2+ 6x+8)2

g’(x) = 0; x = –3;

Xmax = –3; gmax = 19-18+8 = –1.

3) Ψ(x) = x29- x2

D(y): x ≠ ± 3;

Ψ’(x) = 2x • 9- x2+ 2x • x2(9- x2)2 = 18x-2x3+ 2x3(9- x2)2 = 18x(9- x2)2

18x = 0;

x = 0;

Xmin = 0; Ψmin = 0.

4) t(x) = x+1x2- 7

D(y): x ≠ ± 7

t’(x) = x2- 7-2x(x+1)(x2- 7)2 = x2- 7-2x-2x(x2- 7)2 = -x2-2x-7(x2- 7)2

t’(x) = 0; –x2 – 2x – 7 = 0;

D = 4 – 4 • 7 < 0;

Екстремумів нема.