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Popular Functions >

extreme f(x)=x^x

Solution

extreme

Solution

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

Solution steps

f^{'} (x) = x^{x} (ln (x) + 1)

Find intervals:

Decreasing

: 0 < x < \frac{1}{e},

Increasing

: \frac{1}{e} < x < \infty

Plug

x = \frac{1}{e}

into

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

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

Graph

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Frequently Asked Questions (FAQ)

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