§ 37: 37.24

37.24 Знайдіть у точках x₁ = –1 і x₂ = 2 похідну функції:

1) x₁ = –1; f(x) = x² + 4x + 3; f'(x) = 2x + 4; f'(x₁) = 2 • (–1) + 4 = 2;

x₂ = 2; f(x) = x² – 4x + 3; f’(x) = 2x – 4; f’(x₂) = 2 • 2 – 4 = 0.

2) x₁ = –1; x² – 4x + 3 = (–1)² – 4 • (–1) + 3 = 1 + 4 + 3 > 0;

f(x) = x² – 4x + 3; f’(x) = 2x – 4; f’(x₁) = 2 • (–1) – 4 = –6;

x₂ = 2; x² – 4x + 3 = 2² – 4 • 2 + 3 = –1 < 0. f(x) = –x² + 4x – 3;

f’(x) = –2x + 4; f’(x₂) = –2 • 2 + 4 = 0.