Найти при каких значениях x, f (x) = x^4-4x^2+1, f' (x) = 0, f' (x) 0

F (x) = x^4 - 4x^2+1

f ' (x) = 4x^3 - 8x

1) Если f ' (x) = 0

4x^3 - 8x = 0

4x (x^2 - 2) = 0

x (x^2 - 2) = 0

x = 0 или x^2 - 2 = 0

x = √2, x = - √2

Ответ: f ' (x) = 0 при x = √2, x = - √2; x = 0

2) Если f ' (x) < 0

4x^3 - 8x < 0

4x (x^2 - 2) < 0

x = 0 или x^2 - 2 = 0

x = √2, x = - √ 2

x ∈ (- ∞; - √2) ∪ (√2; + ∞)

3) Если f ' (x) > 0

4x^3 - 8x > 0

4x (x^2 - 2) > 0

x = 0 или x^2 - 2 = 0

x = √2, x = - √ 2

x ∈ (-√2; 0) ∪ (√2; + ∞)