What is the extreme x^4-128x^2+9 ?

The extreme x^4-128x^2+9 is Minimum(-8,-4087),Maximum(0,9),Minimum(8,-4087)

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extreme x^4-128x^2+9

extreme

Minimum (- 8, - 4087), Maximum (0, 9), Minimum (8, - 4087)

Solution steps

f^{'} (x) = 4 x^{3} - 256 x

Find intervals:

Decreasing

: - \infty < x < - 8,

Increasing

: - 8 < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 8

into

x^{4} - 128 x^{2} + 9 : - 4087

Minimum (- 8, - 4087)

Plug

x = 0

into

x^{4} - 128 x^{2} + 9 : 9

Maximum (0, 9)

Plug

x = 8

into

x^{4} - 128 x^{2} + 9 : - 4087

Minimum (8, - 4087)

Minimum (- 8, - 4087), Maximum (0, 9), Minimum (8, - 4087)

What is the extreme x^4-128x^2+9 ?
The extreme x^4-128x^2+9 is Minimum(-8,-4087),Maximum(0,9),Minimum(8,-4087)