Відповіді АЛГЕБРА: 24.9 (1-2)

24.9

1) g(x) = 0,25x⁴ – 2x² [–2; 1];

g’(x) = x³ – 4x;

x³ – 4x = 0;

x(x–2)(x + 2) = 0;

x= 0;

x = 2;

x = –2;

g(–2) = 0,25 • 16 – 2 • 4 = –4 – найменше;

g(0) = 0 – найбільше;

g(1) = 0,25 – 2 = –1,75;

2) g(x) = 2x³ – 9x² – 24x + 5; [–3; 0];

g’(x) = 6x² – 18x – 24 = 0;

x² – 3x – 4 = 0;

x₁ = –1; x₂ = 4;

g(–3) = –2 • 27 – 9 • 9 + 24 • 3 + 5 = –58 – найменш.

g(–1) = –2 – 9 + 24 + 5 = 18 найбільше;

g(0) = 5.

3) g(x) = x⁴ – 2x² + 5; [–1; 3];

g‘(x) = 4x³ – 4x;

4x(x² – 1) = 0; x = 0;

x = –1;

x = 1;

g(–1) = 1 – 2 + 5 = 4;

g(0) = 5; найменше;

g(1) = 1 – 2 + 5 = 4;

g(3) = 81 – 18 + 5 = 68 – найбільше;

4) g(x) = x³ + 3x² + 1; [–3; 1];

g’(x) = 3x² + 6x;

3x² + 6x = 0;

3x(x + 2) = 0;

x = 0 x = –2;

g(–3) = –27 + 3 • 9 + 1 = 1 – найменше;

g(–2) = –8 + 12 + 1 = 5 - найб.;

g(0) = 1;

g(1) = 5.