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Popular Functions >

extreme x^4-2x^2

Solution

extreme points

x^{4} - 2 x^{2}

Solution

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

Solution steps

f^{'} (x) = 4 x^{3} - 4 x

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{4} - 2 x^{2} : - 1

Minimum (- 1, - 1)

Plug

x = 0

into

x^{4} - 2 x^{2} : 0

Maximum (0, 0)

Plug

x = 1

into

x^{4} - 2 x^{2} : - 1

Minimum (1, - 1)

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

Graph

Popular Examples

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extreme f(x,y)=x^3+3xy^2-15x+y^3-15y

extreme f(x,y)=e^x-xe^y

extreme x^2y+y^3-27y

Frequently Asked Questions (FAQ)

What is the extreme x^4-2x^2 ?
The extreme x^4-2x^2 is Minimum(-1,-1),Maximum(0,0),Minimum(1,-1)