Відповіді АЛГЕБРА: 24.10 (1-2)

24.10

1) f(x) = 8x² – x⁴ [–1; 2];

f’(x) = 16x – 4x³; 16x – 4x³ = 0;

f(–1) = 8 – 1 = 7; 4x(4 – x²) = 0;

f(0) = 0 – найменше; х = 0; x = 2; x = –2;

f(2) = 8 • 4 – 16 = 16 – найб.

2) f(x) = x³ – 12x² + 45x + 5; [0; 4];

f’(x) = 3x² – 24x + 45;

x² – 8x + 15 = 0;

x₁ = 5; x₂ = 3;

f(0) = 5 найменше;

f(3) = 27 – 12 • 9 + 45 • 3 + 5 = 59;

f(4) = 256 – 12 • 16 + 45 • 4 + 5 = 249 найб.

3) f(x) = 2x² – x⁴ + 3; [–3; 1];

f’(x) = 4x – 4x³

4x(1 – x²) = 0;

4x = 0; 1 – x² = 0;

x = 0; x = ± 1;

f(–3) = 18 – 81 + 3 = –60 найменше;

f(–1) = 4;

f(0) = 3; найбільше;

f(1) = 4;

4) f(x) = x³ – 3x² + 4; [–1; 3];

f’(x) = 3x² – 6x;

3x(x – 2) = 0;

x = 0; x = 2;

f(–1) = –1 – 3 + 4 = 0;

f(0) = 4;

f(2) 8 – 12 + 4 = 0;

f(3) = 27 – 27 + 4 = 4;

Найменше 0, найбільше 4.