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

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

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

extreme

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)^{2} \cdot (x + 4)^{2} : 0

Maximum (- 4, 0)

Plug

x = 0

into

- (x - 4)^{2} \cdot (x + 4)^{2} : - 256

Minimum (0, - 256)

Plug

x = 4

into

- (x - 4)^{2} \cdot (x + 4)^{2} : 0

Maximum (4, 0)

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

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