Let S be the set of all points in (- , ) at which the function, f…

MCQ

Let $S$ be the set of all points in $(-\pi , \pi )$ at which the function, $f(x) = min\, \{sin\,x, cos\,x\}$ is non-differentiable. Then $S$ is a subset of which of the following?

A
$\left\{ { - \frac{\pi }{4},0,\frac{\pi }{4}} \right\}$
✓
$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}$
C
$\left\{ { - \frac{\pi }{2}, - \frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2}} \right\}$
D
$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{2},\frac{\pi }{2},\frac{{3\pi }}{4}} \right\}$

✓

Answer

Correct option: B.

$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}$

b
Hence number of points where $f(x)$ is non-differentiable are $2$

which are $\frac{{ - 3\pi }}{4}$ and $\frac{\pi }{4}$

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