JEE Mains · Maths · STD 12 - 5. continuity and differentiation
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 \(\left\{ { - \frac{\pi }{4},0,\frac{\pi }{4}} \right\}\)
- B \(\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}\)
- 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 & Solution
Correct Answer
(B) \(\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}\)
Step-by-step Solution
Detailed explanation
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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