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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 64)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 2

into

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

Minimum (2, - 64)

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

\frac{1}{3} cos (x)

f (x) = \frac{8 x - 3}{4}

f (x) = 2 x^{3} - 24 x

\frac{tan ( x )}{x ^{2}}

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

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