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

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

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

extreme points

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

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

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} : - 2

Minimum (- 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

Maximum (1, 2)

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

f (x) = ln (5 - 2 x^{2})

f (x) = 2 x^{3} - \frac{11}{2} x^{2} - 10 x + 2

f (x, y) = 8 y^{2} + 5 x^{2} - 10 y + 6 x - 10

f (x) = 8 x^{5} - 120 x^{3} + 43

f (x) = \frac{x ^{2}}{x ^{4} + 1}

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