What is the extreme f(x)=4x^4-24x^2 ?

The extreme f(x)=4x^4-24x^2 is Minimum(-sqrt(3),-36),Maximum(0,0),Minimum(sqrt(3),-36)

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extreme f(x)=4x^4-24x^2

extreme points

f (x) = 4 x^{4} - 24 x^{2}

Minimum (- 3, - 36), Maximum (0, 0), Minimum (3, - 36)

Solution steps

f^{'} (x) = 16 x^{3} - 48 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

4 x^{4} - 24 x^{2} : - 36

Minimum (- 3, - 36)

Plug

x = 0

into

4 x^{4} - 24 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

4 x^{4} - 24 x^{2} : - 36

Minimum (3, - 36)

Minimum (- 3, - 36), Maximum (0, 0), Minimum (3, - 36)

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

4

(5, 0), (2, - 2)

f (x) = 30 - x^{2} + x

f (x) = - 5 x + 20

What is the extreme f(x)=4x^4-24x^2 ?
The extreme f(x)=4x^4-24x^2 is Minimum(-sqrt(3),-36),Maximum(0,0),Minimum(sqrt(3),-36)