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

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

Popular >

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

extreme points

f (x) = - 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)

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

f (x, y) = x^{2} + y^{2} + 4 x - 2 y + 6

f (x) = \frac{4860}{x} + 18 x + 724924

f (x) = 3 x 4 - 3 x

x^{2} + y^{2} + 4 x + 20

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