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

The extreme f(x)=3x^5-5x^3 is Maximum(-1,2),Saddle(0,0),Minimum(1,-2)

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

extreme points

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

Maximum (- 1, 2), Saddle (0, 0), Minimum (1, - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

3 x^{5} - 5 x^{3} : 2

Maximum (- 1, 2)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

3 x^{5} - 5 x^{3} : - 2

Minimum (1, - 2)

Maximum (- 1, 2), Saddle (0, 0), Minimum (1, - 2)

\frac{2 x ^{3}}{3} - x^{2} + \frac{x}{2} + \frac{1}{3}

y = \frac{2}{x}

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

f (x) = 2 x - 7

- \frac{1}{2} x + 3

What is the extreme f(x)=3x^5-5x^3 ?
The extreme f(x)=3x^5-5x^3 is Maximum(-1,2),Saddle(0,0),Minimum(1,-2)