What is the extreme f(x)=20x^3-3x^5 ?

The extreme f(x)=20x^3-3x^5 is Minimum(-2,-64),Saddle(0,0),Maximum(2,64)

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extreme f(x)=20x^3-3x^5

extreme points

f (x) = 20 x^{3} - 3 x^{5}

Minimum (- 2, - 64), Saddle (0, 0), Maximum (2, 64)

Solution steps

f^{'} (x) = 60 x^{2} - 15 x^{4}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

20 x^{3} - 3 x^{5} : - 64

Minimum (- 2, - 64)

Plug

x = 0

into

20 x^{3} - 3 x^{5} : 0

Saddle (0, 0)

Plug

x = 2

into

20 x^{3} - 3 x^{5} : 64

Maximum (2, 64)

Minimum (- 2, - 64), Saddle (0, 0), Maximum (2, 64)

What is the extreme f(x)=20x^3-3x^5 ?
The extreme f(x)=20x^3-3x^5 is Minimum(-2,-64),Saddle(0,0),Maximum(2,64)