What is the extreme f(x)=-x^4+32x^2-256 ?

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

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extreme f(x)=-x^4+32x^2-256

extreme points

f (x) = - x^{4} + 32 x^{2} - 256

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

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

Maximum (- 4, 0)

Plug

x = 0

into

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

Minimum (0, - 256)

Plug

x = 4

into

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

Maximum (4, 0)

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

(- 2.4) (3.9)

f (x) = 2 x (\frac{500}{3} - \frac{4}{3} x)

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

y = - 2 x + 2.5

y = x^{2} - 4

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