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Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiability1 Mark
MCQ
The function $\text{f(x)}=|\cos\text{x}|$ is:
  • A
    Everywhere continuous and differentiable.
  • ✓
    Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  • C
    Neither continuous nor differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  • D
    None of these.
✓

Answer

Correct option: B.
Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
As cos x is even function it is continuous everywhere but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
$\cos\Big[(2\text{n}+1)\frac{\pi}{2}=\cos\Big(\text{n}\pi+\frac{\pi}{2}\Big)=-\sin\text{n}\pi$
For n as an integer $\Rightarrow\sin\text{n}\pi=0$
For n as rational $\Rightarrow\sin\text{n}\pi=-1$

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