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Popular Functions >

extreme x^4-2x^2+2

Solution

extreme points

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

Solution

Minimum (- 1, 1), Maximum (0, 2), 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} + 2 : 1

Minimum (- 1, 1)

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = 1

into

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

Minimum (1, 1)

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

Graph

Popular Examples

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extreme f(x,y)=xy+y

Frequently Asked Questions (FAQ)

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