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Popular Functions >

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

Solution

extreme points

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

Solution

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

Maximum (- 1, 3)

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 : - 1

Minimum (1, - 1)

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

Graph

Popular Examples

extreme f(x)=2x^2+3xy+4y^2-2x+10y

extreme f(x)=x^4-8x^3-6

extreme f(x)=x(17-2x)(50/2-x)

extreme f(x,y)=9y^2-3x^2-10y+5xy

extreme f(x)=x^3-5x^2+3x+12,(-2,4)

Frequently Asked Questions (FAQ)

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