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Popular Functions >

extreme f(x)=2(5x)^x

Solution

extreme points

f (x) = 2 (5 x)^{x}

Solution

Minimum (\frac{1}{5 e}, 2 (\frac{1}{e})^{\frac{1}{5 e}})

Solution steps

f^{'} (x) = 2 (ln (5 x) + 1) (5 x)^{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{5 e},

Increasing

: \frac{1}{5 e} < x < \infty

Plug

x = \frac{1}{5 e}

into

2 (5 x)^{x} : 2 (\frac{1}{e})^{\frac{1}{5 e}}

Minimum (\frac{1}{5 e}, 2 (\frac{1}{e})^{\frac{1}{5 e}})

Graph

Popular Examples

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f (x, y) = 400 - 16 x^{2} - 81 y^{2}

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extreme 3x+3 extreme points

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extreme (x-2)^3+1 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2(5x)^x ?
The extreme f(x)=2(5x)^x is Minimum(1/(5e),2(1/e)^{1/(5e)})