F x - x x has stationary point atA- x - eB- x -1- pC- x -1D- x - e

The correct option is B x=1/e nbsp; nbsp; nbsp;f(x)=x^x ⇒log f(x)=xlog x nbsp; nbsp; Differentiating wrt x, we get f'(x)/f(x)=log x +1 ⇒ f'(x)=x^x(1 ...

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Standard XII

Mathematics

Local Maxima

f x = x x has...

Question

$f (x) = x^{x}$ has stationary point at

x = e

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x = \frac{1}{e}

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x = 1

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x = \sqrt{e}

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Solution

The correct option is B $x = \frac{1}{e}$
$f (x) = x^{x}$
$\Rightarrow log f (x) = x log x$
Differentiating wrt $x$ , we get
$\frac{f^{'} (x)}{f (x)} = log x + 1$
$\Rightarrow f^{'} (x) = x^{x} (1 + log x)$
Put $f^{'} (x) = 0$ , we get $x = \frac{1}{e}$
$∴ f (x)$ has stationary point at $x = \frac{1}{e}$ .

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f(x)=xx has stationary point at

The correct option is B x=1e f(x)=xx ⇒logf(x)=xlogx Differentiating wrt x, we get f′(x)f(x)=logx+1 ⇒f′(x)=xx(1+logx) Put f′(x)=0, we get x=1e ∴f(x) has stationary point at x=1e.

$f (x) = x^{x}$ has stationary point at