What is the extreme f(x)=x^4-2x^2=x^2(x^2-2) ?

The extreme f(x)=x^4-2x^2=x^2(x^2-2) is Minimum(-1,-1),Maximum(0,0),Minimum(1,-1)

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extreme f(x)=x^4-2x^2=x^2(x^2-2)

extreme

Minimum (- 1, - 1), Maximum (0, 0), Minimum (1, - 1)

Solution steps

f^{'} (x) = 4 x (x + 1) (x - 1)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{2} (x^{2} - 2) : - 1

Minimum (- 1, - 1)

Plug

x = 0

into

x^{2} (x^{2} - 2) : 0

Maximum (0, 0)

Plug

x = 1

into

x^{2} (x^{2} - 2) : - 1

Minimum (1, - 1)

Minimum (- 1, - 1), Maximum (0, 0), Minimum (1, - 1)

What is the extreme f(x)=x^4-2x^2=x^2(x^2-2) ?
The extreme f(x)=x^4-2x^2=x^2(x^2-2) is Minimum(-1,-1),Maximum(0,0),Minimum(1,-1)