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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
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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