What is the extreme f(x)=3x^5-5x^3+1 ?

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

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extreme f(x)=3x^5-5x^3+1

extreme points

f (x) = 3 x^{5} - 5 x^{3} + 1

Maximum (- 1, 3), Saddle (0, 1), Minimum (1, - 1)

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} + 1 : 3

Maximum (- 1, 3)

Plug

x = 0

into

3 x^{5} - 5 x^{3} + 1 : 1

Saddle (0, 1)

Plug

x = 1

into

3 x^{5} - 5 x^{3} + 1 : - 1

Minimum (1, - 1)

Maximum (- 1, 3), Saddle (0, 1), Minimum (1, - 1)

f (x) = x^{3} + 3 x^{2} - 9 x + 5

f (x) = 5 x^{3} + 2 x^{2} - 3 x

f (x) = \frac{x}{x ^{2} + y ^{2}}

f (x) = \frac{- 12 x ^{3} + x}{x}

\frac{e ^{x}}{1 - e ^{x}}

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