What is the extreme f(x)=-x^4+6x^2 ?

The extreme f(x)=-x^4+6x^2 is Maximum(-sqrt(3),9),Minimum(0,0),Maximum(sqrt(3),9)

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extreme f(x)=-x^4+6x^2

extreme points

f (x) = - x^{4} + 6 x^{2}

Maximum (- 3, 9), Minimum (0, 0), Maximum (3, 9)

Solution steps

f^{'} (x) = - 4 x^{3} + 12 x

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- x^{4} + 6 x^{2} : 9

Maximum (- 3, 9)

Plug

x = 0

into

- x^{4} + 6 x^{2} : 0

Minimum (0, 0)

Plug

x = 3

into

- x^{4} + 6 x^{2} : 9

Maximum (3, 9)

Maximum (- 3, 9), Minimum (0, 0), Maximum (3, 9)

What is the extreme f(x)=-x^4+6x^2 ?
The extreme f(x)=-x^4+6x^2 is Maximum(-sqrt(3),9),Minimum(0,0),Maximum(sqrt(3),9)