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Popular >

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

Solution

extreme points

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

Solution

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)

Graph

Popular Examples

extreme p(x)=3x^3-10x^2+ax-2 extreme points

p (x) = 3 x^{3} - 10 x^{2} + a x - 2

extreme f(x)=(x^3-4)/(x-1)extreme points

f (x) = \frac{x ^{3} - 4}{x - 1}

extreme f(x)=-2/3 x^3+10x^2-48x-1 extreme points

f (x) = - \frac{2}{3} x^{3} + 10 x^{2} - 48 x - 1

extreme f(x)=4x-48x^{1/3}extreme points

f (x) = 4 x - 48 x^{\frac{1}{3}}

extreme f(x,y)=4x^2+3y^2+3xy-10x+6y+36 extreme points

f (x, y) = 4 x^{2} + 3 y^{2} + 3 x y - 10 x + 6 y + 36

Frequently Asked Questions (FAQ)

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