What is the extreme x^4-32x^2+256 ?

The extreme x^4-32x^2+256 is Minimum(-4,0),Maximum(0,256),Minimum(4,0)

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extreme x^4-32x^2+256

extreme points

x^{4} - 32 x^{2} + 256

Minimum (- 4, 0), Maximum (0, 256), Minimum (4, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 64 x

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 4

into

x^{4} - 32 x^{2} + 256 : 0

Minimum (- 4, 0)

Plug

x = 0

into

x^{4} - 32 x^{2} + 256 : 256

Maximum (0, 256)

Plug

x = 4

into

x^{4} - 32 x^{2} + 256 : 0

Minimum (4, 0)

Minimum (- 4, 0), Maximum (0, 256), Minimum (4, 0)

f (x) = \frac{1}{1 + x ^{2}}

y = 4 x^{3}

f (x) = x + \frac{17}{x}

f (x) = 5 x^{2}

(- 1, 5), (- 1, - 3)

What is the extreme x^4-32x^2+256 ?
The extreme x^4-32x^2+256 is Minimum(-4,0),Maximum(0,256),Minimum(4,0)