Найти значение х, при которых значение производной функции f (x) = 0, если f (x) = x^4+4x³-8x²-5

F ' (x) = (x^4 + 4x^3 - 8x^2 - 5) ' = 4x^3 + 12x^2 - 16x

f ' (x) = 0

4x^3 + 12x^2 - 16x = 0 / : 4

x^3 + 3x^2 - 4x = 0

x (x^2 + 3x - 4) = 0

1) x1 = 0;

2) x^2 + 3x - 4 = 0

D = 9 + 16 = 25

x2 = ( - 3 + 5) / 2 = 2/2 = 1

x3 = ( - 3 - 5) / 2 = - 8/2 = - 4

Ответ

- 4; 0; 1

(x) = x^4+4x^3-8x^2-5f' (x) = 4x³ + 12x² - 16x 4x³ + 12x² - 16x = 04x (x² + 3x - 4) = 0x₁ = 0x² + 3x - 4 = 0x₂ = - 4x₃ = 1