What is the extreme y=-3x^5+5x^3+1 ?

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

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extreme y=-3x^5+5x^3+1

extreme points

y = - 3 x^{5} + 5 x^{3} + 1

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - 1)

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 : 3

Maximum (1, 3)

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

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