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

The extreme f(x)=x^4-2x^2-4 is Minimum(-1,-5),Maximum(0,-4),Minimum(1,-5)

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

extreme points

f (x) = x^{4} - 2 x^{2} - 4

Minimum (- 1, - 5), Maximum (0, - 4), Minimum (1, - 5)

Solution steps

f^{'} (x) = 4 x^{3} - 4 x

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{4} - 2 x^{2} - 4 : - 5

Minimum (- 1, - 5)

Plug

x = 0

into

x^{4} - 2 x^{2} - 4 : - 4

Maximum (0, - 4)

Plug

x = 1

into

x^{4} - 2 x^{2} - 4 : - 5

Minimum (1, - 5)

Minimum (- 1, - 5), Maximum (0, - 4), Minimum (1, - 5)

What is the extreme f(x)=x^4-2x^2-4 ?
The extreme f(x)=x^4-2x^2-4 is Minimum(-1,-5),Maximum(0,-4),Minimum(1,-5)