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Popular >

extreme x^2+x^{-2}

Solution

extreme points

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

Solution

Minimum (- 1, 2), Minimum (1, 2)

Solution steps

f^{'} (x) = 2 x - \frac{2}{x ^{3}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, 2)

Plug

x = 1

into

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

Minimum (1, 2)

Minimum (- 1, 2), Minimum (1, 2)

Popular Examples

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extreme f(x)=6x^2-6x+9 extreme points

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extreme f(x)=2y^2+2xy+x^2-16x-20y extreme points

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extreme-2/(4x+x^2-2)extreme points

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

extreme f(x)=4x^3+9x^2 extreme points

f (x) = 4 x^{3} + 9 x^{2}

Frequently Asked Questions (FAQ)

What is the extreme x^2+x^{-2} ?
The extreme x^2+x^{-2} is Minimum(-1,2),Minimum(1,2)