What is the extreme f(x)=-3x^4+12x^2-9 ?

The extreme f(x)=-3x^4+12x^2-9 is Maximum(-sqrt(2),3),Minimum(0,-9),Maximum(sqrt(2),3)

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extreme f(x)=-3x^4+12x^2-9

extreme points

f (x) = - 3 x^{4} + 12 x^{2} - 9

Maximum (- 2, 3), Minimum (0, - 9), Maximum (2, 3)

Solution steps

f^{'} (x) = - 12 x^{3} + 24 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- 3 x^{4} + 12 x^{2} - 9 : 3

Maximum (- 2, 3)

Plug

x = 0

into

- 3 x^{4} + 12 x^{2} - 9 : - 9

Minimum (0, - 9)

Plug

x = 2

into

- 3 x^{4} + 12 x^{2} - 9 : 3

Maximum (2, 3)

Maximum (- 2, 3), Minimum (0, - 9), Maximum (2, 3)

What is the extreme f(x)=-3x^4+12x^2-9 ?
The extreme f(x)=-3x^4+12x^2-9 is Maximum(-sqrt(2),3),Minimum(0,-9),Maximum(sqrt(2),3)