What is the extreme f(x)=-x^4+8x^2-8 ?

The extreme f(x)=-x^4+8x^2-8 is Maximum(-2,8),Minimum(0,-8),Maximum(2,8)

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extreme f(x)=-x^4+8x^2-8

extreme points

f (x) = - x^{4} + 8 x^{2} - 8

Maximum (- 2, 8), Minimum (0, - 8), Maximum (2, 8)

Solution steps

f^{'} (x) = - 4 x^{3} + 16 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- x^{4} + 8 x^{2} - 8 : 8

Maximum (- 2, 8)

Plug

x = 0

into

- x^{4} + 8 x^{2} - 8 : - 8

Minimum (0, - 8)

Plug

x = 2

into

- x^{4} + 8 x^{2} - 8 : 8

Maximum (2, 8)

Maximum (- 2, 8), Minimum (0, - 8), Maximum (2, 8)

What is the extreme f(x)=-x^4+8x^2-8 ?
The extreme f(x)=-x^4+8x^2-8 is Maximum(-2,8),Minimum(0,-8),Maximum(2,8)