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

The extreme f(x)=x^4-24x^2 is Minimum(-2sqrt(3),-144),Maximum(0,0),Minimum(2sqrt(3),-144)

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

extreme points

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

Minimum (- 23, - 144), Maximum (0, 0), Minimum (23, - 144)

Solution steps

f^{'} (x) = 4 x^{3} - 48 x

Find intervals:

Decreasing

: - \infty < x < - 23,

Increasing

: - 23 < x < 0,

Decreasing

: 0 < x < 23,

Increasing

: 23 < x < \infty

Plug

x = - 23

into

x^{4} - 24 x^{2} : - 144

Minimum (- 23, - 144)

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 23

into

x^{4} - 24 x^{2} : - 144

Minimum (23, - 144)

Minimum (- 23, - 144), Maximum (0, 0), Minimum (23, - 144)

What is the extreme f(x)=x^4-24x^2 ?
The extreme f(x)=x^4-24x^2 is Minimum(-2sqrt(3),-144),Maximum(0,0),Minimum(2sqrt(3),-144)