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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2019 · 12 January · Morning Shift · Mathematics · Continuity and Differentiability

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

Let SS be the set of all points in (−π,π)\left(- \pi, \pi\right) at which the function, f(x)=min{sin⁡x,cos⁡x}isnotdifferentiable.Thenf\left(x\right) = min\left\{\sin x, \cos x\right\} is not differentiable. ThenSisasubsetofwhichofthefollowing?is a subset of which of the following?Let S be the set of all points in (- π, π) at which the function, f(x) = min\ x, x\ is not differentiable. Then S is a

Options

  1. A{−3π4,−π2,π2,3π4}\left\{- \dfrac{3\pi}{4}, - \dfrac{\pi}{2}, \dfrac{\pi}{2}, \dfrac{3\pi}{4}\right\}
  2. B{−3π4,−π4,3π4,π4}\left\{- \dfrac{3\pi}{4}, - \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{\pi}{4}\right\}
  3. C{−π4,0,π4}\left\{- \dfrac{\pi}{4}, 0, \dfrac{\pi}{4}\right\}
  4. D{−π2,−π4,π4,π2}\left\{- \dfrac{\pi}{2}, - \dfrac{\pi}{4}, \dfrac{\pi}{4}, \dfrac{\pi}{2}\right\}

Correct answer

B. {−3π4,−π4,3π4,π4}\left\{- \dfrac{3\pi}{4}, - \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{\pi}{4}\right\}

Step-by-step solution

Let S be the set of all points in (- π, π) at which the function, f(x) = min\ x, x\ is not differentiable. Then S is a

Sharp points are at −3π4\dfrac{- 3\pi}{4} and π4\dfrac{\pi}{4}.

∴∴ Set of non-differentiable points of function are \left\{- \dfrac{3\pi}{4}, \dfrac{\pi}{4}\right\}whichisasubsetof{−3π4,−π4,3π4,π4}which is a subset of \left\{- \dfrac{3\pi}{4}, - \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{\pi}{4}\right\}.

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