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

The extreme f(x)=x^2(2-x^2) is Maximum(-1,1),Minimum(0,0),Maximum(1,1)

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

extreme points

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

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

Solution steps

f^{'} (x) = - 4 x (x + 1) (x - 1)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

x^{2} (2 - x^{2}) : 1

Maximum (- 1, 1)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

x^{2} (2 - x^{2}) : 1

Maximum (1, 1)

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

What is the extreme f(x)=x^2(2-x^2) ?
The extreme f(x)=x^2(2-x^2) is Maximum(-1,1),Minimum(0,0),Maximum(1,1)