f(x)=x^x has a stationary point at - Vidyadip

MCQ

$f(x)=x^x$ has a stationary point at

A
$x=e$
✓
$x=\frac{1}{e}$
C
$x=1$
D
$x=\sqrt{e}$

✓

Answer

Correct option: B.

$x=\frac{1}{e}$

(b) : We have, $f(x)=x^x$
$\Rightarrow f^{\prime}(x)=x^x(1+\log x)$
For stationary point, $f^{\prime}(x)=0$
$
\Rightarrow x^x(1+\log x)=0 \Rightarrow x=\frac{1}{e}
$

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