Відповіді АЛГЕБРА: 22.12 (1-2)

22.12

1) f(x) = 2xx+2

D(y): x ≠ –2;

f’(x) = 2x+2- 2x(x+2)2 = 4(x+2)2 ≠ 0;

Екстремумів нема;

2) φ(х) = x9 + 4x

D(y): x ≠ 0;

φ’(x) = 19 – 4x2 = 0;

x2- 369x2 = 0;

x = ±6;

Xmax = –6; φmax = –69 + 4-6 = –23 – 23 = –43

Xmin = 6; φmin = 69 + 46 = 23 + 23 = 43

3) Ψ(x) = xx2+ 4

D(y): R

Ψ’(x) = x2+ 4-2x • x(x2+ 4)2 = 4- x2(x2+ 4)2

Ψ’(x) = 0 4 – x2 = 0

x = 2 або x = –2

Xmin = –2

Ψmin = -24+4 = –28 = –14

xmax = 2;

Ψ max = 24+4 = 28 = 14

4) p(x) = x – 2x;

D(y): x ≥ 0;

p’(x) = 1 – 22x = 1 – 1x = 0

Xmin = 1; pmin = 1 – 21 = –1.