Відповіді АЛГЕБРА: 22.10 (1)

22.10

1) y = 2x³ + 6x² – 18x;

y’ = 6x² + 12x – 18;

y’ = 0;

6x² + 12x – 18 = 0;

x² + 2x – 3 = 0;

x₁ = 1; x₂ = –3;

Xmax = –3;

ymax = 2 • (–3)³ + 6 • (–3)² – 18 • (–3) = –54 + 54 + 54 = 54;

Xmin = 1;

ymin = 2 • 1³ + 6 • 1² – 18 = 8 – 18 = –10.

2) y = 2 + 12x + 9x² – 10x³

y’ = 12 + 18x – 30x²

12 + 18x – 30x² = 0 |: (–6);

5x² – 3x – 2 = 0;

D = 9 + 4 • 10 = 49;

x₁ = 3+710 = 1; x₂ = 3-710 = –410 = –25

Xmin = –25 ymin = 2 – 245 + 9 • 425 – 10 • (–8125) = 2 – 4,8 + 1,44 +

+ 0,64 = –0,72;

Xmax = 1 ymax = 2 + 12 + 9 – 10 = 13.

3) y – x³ – 3x;

y’ = 3x² – 3;

3x² – 3 = 0;

x = ± 1;

Xmax = –1; ymax = (–1)³ – 3 • (–1) = –1 + 3 = 2;

Xmin = 1; ymin = 1 – 3 = –2.

4) y = x⁴ – 2x² + 3;

y’ = 4x³ – 4x;

4x(x² – 1) = 0; x = 0; x = 1; x = –1;

Xmax = 0; ymax = 3;

Xmin = –1; Xmin = 1; ymin = 1 – 2 + 3 = 2.