Відповіді АЛГЕБРА: 22.9 (1)

22.9

1) y = x³ – 6x² – 15x + 3;

y’ = 3x² – 12x – 15;

3x² – 12x – 15 = 0;

x² – 4x – 5 = 0;

x₁ = –1; x₂ = 5;

Xmax = –1;

ymax = (–1)³ – 6 • (–1)² – 15 • (–1) + 3 = –1 – 6 + 15 + 3 = 11;

Xmin = 5;

ymin = 5³ – 6 • 5² – 15 • 5 + 3 = 125 – 150 – 75 + 3 = –97.

2) y = 1 + 18x + 15x² – 4x³

y’ = 18 + 30x – 12x²;

–12x² + 30x + 18 = 0 |: (–6);

2x² – 5x – 3 = 0;

D = 25 + 4 • 2 • 3 = 25 + 24 = 49;

x₁ = 5+74 = 124 = 3; x₂ = –12

Xmax = –12

ymax = 1 – 9 + 15 • 14 + 4 • 18 = –8 + 154 + 12 = –3,75;

Xmin = 3;

ymin = 1 + 54 + 15 • 9 – 4 • 27 = 190 – 108 = –82.

3) y = x – 3x³

y’ = 1 – 9x²

1 – 9x² = 0 |: (–1);

(3x – 1)(3x + 1) = 0;

x = 13 x = –13

Xmin = –13

ymin = –13 – 3 • (–13)³ = –1\33 + 1\19 = -3+19 = –29

Xmax = 13

ymax = 13 – 3 • 133 = 13 – 19 = 29

4) y = 14x⁴ – 2x²

y’ = x³ – 4x = 0;

x(x – 2)(x + 2) = 0; x = 0, x = 2, x = –2;

Xmax = 0; ymax = 0;

Xmin = –2; Xmin = 2; ymin = 14 • 2⁴ – 2 • 2² = 4 – 8 = –4.