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Graphical Interpretation of Differentiability

Let S be the ...

Question

Let $S$ be the set of all points in $(- π, π)$ at which the function, $f (x)$ = min ${sin x, cos x}$ is not differentiable. Then $S$ is a subset of which of the following?

{- \frac{π}{2}, - \frac{π}{4}, \frac{π}{4}, \frac{π}{2}}

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{- \frac{3 π}{4}, - \frac{π}{4}, \frac{3 π}{4}, \frac{π}{4}}

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{- \frac{3 π}{4}, - \frac{π}{2}, \frac{π}{2}, \frac{3 π}{4}}

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{- \frac{π}{4}, 0, \frac{π}{4}}

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Solution

The correct option is B ${- \frac{3 π}{4}, - \frac{π}{4}, \frac{3 π}{4}, \frac{π}{4}}$
$f (x)$ = min ${sin x, cos x}$

$∴$ $f (x)$ is not differentiable at
$x = - \frac{3 π}{4}, \frac{π}{4}$
Hence, $S = {- \frac{3 π}{4}, \frac{π}{4}}$

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