What is the extreme f(x)=-(25-x^2)^2 ?

The extreme f(x)=-(25-x^2)^2 is Maximum(-5,0),Minimum(0,-625),Maximum(5,0)

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extreme f(x)=-(25-x^2)^2

extreme

Maximum (- 5, 0), Minimum (0, - 625), Maximum (5, 0)

Solution steps

f^{'} (x) = - 4 x^{3} + 100 x

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

- (25 - x^{2})^{2} : 0

Maximum (- 5, 0)

Plug

x = 0

into

- (25 - x^{2})^{2} : - 625

Minimum (0, - 625)

Plug

x = 5

into

- (25 - x^{2})^{2} : 0

Maximum (5, 0)

Maximum (- 5, 0), Minimum (0, - 625), Maximum (5, 0)

What is the extreme f(x)=-(25-x^2)^2 ?
The extreme f(x)=-(25-x^2)^2 is Maximum(-5,0),Minimum(0,-625),Maximum(5,0)