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

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

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

extreme points

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

Maximum (- 1, 5), Saddle (0, 3), 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} + 3 : 5

Maximum (- 1, 5)

Plug

x = 0

into

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

Saddle (0, 3)

Plug

x = 1

into

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

Minimum (1, 1)

Maximum (- 1, 5), Saddle (0, 3), Minimum (1, 1)

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