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Popular >

extreme f(x)=x^{(1/x)}

Solution

extreme points

f (x) = x^{(\frac{1}{x})}

Solution

Maximum (e, e^{\frac{1}{e}})

Solution steps

f^{'} (x) = x^{\frac{1 - 2 x}{x}} (- ln (x) + 1)

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = e

into

x^{\frac{1}{x}} : e^{\frac{1}{e}}

Maximum (e, e^{\frac{1}{e}})

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^{(1/x)} ?
The extreme f(x)=x^{(1/x)} is Maximum(e,e^{1/e})