What is the extreme 20x^4-120x^2 ?

The extreme 20x^4-120x^2 is Minimum(-sqrt(3),-180),Maximum(0,0),Minimum(sqrt(3),-180)

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extreme 20x^4-120x^2

extreme points

20 x^{4} - 120 x^{2}

Minimum (- 3, - 180), Maximum (0, 0), Minimum (3, - 180)

Solution steps

f^{'} (x) = 80 x^{3} - 240 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

20 x^{4} - 120 x^{2} : - 180

Minimum (- 3, - 180)

Plug

x = 0

into

20 x^{4} - 120 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

20 x^{4} - 120 x^{2} : - 180

Minimum (3, - 180)

Minimum (- 3, - 180), Maximum (0, 0), Minimum (3, - 180)

What is the extreme 20x^4-120x^2 ?
The extreme 20x^4-120x^2 is Minimum(-sqrt(3),-180),Maximum(0,0),Minimum(sqrt(3),-180)