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Popular >

extreme f(x)=(2x)^x

Solution

extreme points

f (x) = (2 x)^{x}

Solution

Minimum (\frac{1}{2 e}, (\frac{1}{e})^{\frac{1}{2 e}})

Solution steps

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

Find intervals:

Decreasing

: 0 < x < \frac{1}{2 e},

Increasing

: \frac{1}{2 e} < x < \infty

Plug

x = \frac{1}{2 e}

into

(2 x)^{x} : (\frac{1}{e})^{\frac{1}{2 e}}

Minimum (\frac{1}{2 e}, (\frac{1}{e})^{\frac{1}{2 e}})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(2x)^x ?
The extreme f(x)=(2x)^x is Minimum(1/(2e),(1/e)^{1/(2e)})