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

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

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

extreme points

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

Maximum (- 2, 4), Minimum (0, 0), Maximum (2, 4)

Solution steps

f^{'} (x) = - 4 x^{3} + 8 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 4)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 2

into

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

Maximum (2, 4)

Maximum (- 2, 4), Minimum (0, 0), Maximum (2, 4)

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