Відповіді АЛГЕБРА: 23.6 (1)

23.6

1) f(x) = x³ – 3x²

1) D(y): R;

2) f(–x) = (–x)³ – 3 • (–x)² = –x³ – 3x²

Ні парна, ні непарна;

3) Ox: y = 0; x³ – 3x² = 0;

x²(x – 3) = 0;

x = 0; x = 3;

Oy: x = 0; y = 0;

4) f’(x) = 3x² – 6x;

3x² – 6x = 0;

3x(x – 2) = 0;

x = 0; x = 2;

Xmin = 2; Xmax = 0;

ymin = 8 – 3 • 4 = –4; ymax = 0;

2) f(x) = 13x3 – 3x;

D(y): R;

f(–x) = 13 • (–x)3 – 3 • (–x) = –13x3 + 3x непарна;

Ox: y = 0; 13x3 – 3x = 0;

x³ – 9x = 0;

x(x – 3)(x + 3) = 0;

x = 0; x = 3; x = –3;

Oy: x = 0; y = 0;

f’(x) = x² – 3;

x² – 3 = 0;

x = ± 3

Xmax = –3

ymax = 13 • (–33) + 33 = –3 + 33 = 23

Xmin = 3

ymin = –23

3) f(x) = x⁴ – 43x³

D(y): R;

f(–x) = (–x)⁴ – 43 • (–x)³ ні парна, ні непарна;

Ox: y = 0; x⁴ – 43x³ = 0;

x³(x – 43) = 0; x = 0; x = 43

Oy: x = 0; y = 0;

f’(x) = 4x³ – 4x² = 0;

4x²(x – 1) = 0;

x = 0; x = 1;

Xmin = 1; ymin = 1 – 43 = –13

4) f(x) = 2x + 4x⁴

D(y): R;

f(–x) = –2x + 4x⁴ ні парна, ні непарна;

Ox: y = 0; 2x + 4x⁴ = 0;

2x(1 + 2x³) = 0;

x = 0; x = 312

Oy: x = 0; y = 0;

f’(x) = 2 + 16x³

2 + 16x³ = 0;

x³ = –18

x = –12

Xmin = –12

ymin = –1 + 4 • 116 = –1 + 14 = –34