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Popular >

extreme f(x)=x^x

Solution

extreme points

f (x) = x^{x}

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}})

Popular Examples

inverse of f(x)= 1/x-3 inverse

f (x) = \frac{1}{x} - 3

parity f(x)= 1/(x^2+9)parity

f (x) = \frac{1}{x ^{2} + 9}

inverse of f(x)=2^{-(x+13)}+1 inverse

f (x) = 2^{- (x + 13)} + 1

inverse of f(x)=(2x-3)/(3-x)inverse

f (x) = \frac{2 x - 3}{3 - x}

inverse of f(x)=-3x+2 inverse

f (x) = - 3 x + 2

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})