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Popular >

extreme f(x)=2(4x)^x

Solution

extreme points

f (x) = 2 (4 x)^{x}

Solution

Minimum (\frac{1}{4 e}, 2 (\frac{1}{e})^{\frac{1}{4 e}})

Solution steps

f^{'} (x) = 2 (ln (4 x) + 1) (4 x)^{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{4 e},

Increasing

: \frac{1}{4 e} < x < \infty

Plug

x = \frac{1}{4 e}

into

2 (4 x)^{x} : 2 (\frac{1}{e})^{\frac{1}{4 e}}

Minimum (\frac{1}{4 e}, 2 (\frac{1}{e})^{\frac{1}{4 e}})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2(4x)^x ?
The extreme f(x)=2(4x)^x is Minimum(1/(4e),2(1/e)^{1/(4e)})