What is the extreme f(x)=(4-x^2)^5 ?

The extreme f(x)=(4-x^2)^5 is Saddle(-2,0),Maximum(0,1024),Saddle(2,0)

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extreme f(x)=(4-x^2)^5

extreme points

f (x) = (4 - x^{2})^{5}

Saddle (- 2, 0), Maximum (0, 1024), Saddle (2, 0)

Solution steps

f^{'} (x) = - 10 x (4 - x^{2})^{4}

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

(4 - x^{2})^{5} : 0

Saddle (- 2, 0)

Plug

x = 0

into

(4 - x^{2})^{5} : 1024

Maximum (0, 1024)

Plug

x = 2

into

(4 - x^{2})^{5} : 0

Saddle (2, 0)

Saddle (- 2, 0), Maximum (0, 1024), Saddle (2, 0)

What is the extreme f(x)=(4-x^2)^5 ?
The extreme f(x)=(4-x^2)^5 is Saddle(-2,0),Maximum(0,1024),Saddle(2,0)