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Maths-

General

Easy

Question

Let $f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets$ , then which of the following is true?

$f^{}$ '/> is increasing in $(- \frac{π}{2}, 0)$ and decreasing in $(0, \frac{π}{2})$
$f^{}$ (0)=-π2'/>
$f$ is not differentiable at $x = 0$
$f$ is decreasing in $(- \frac{π}{2}, 0)$ and increasing in $(0, \frac{π}{2})$

The correct answer is: $f$ is not differentiable at $x equals 0$

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