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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
    Differentiable at$\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  • ✓
    Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  • C
    Neither differentiable nor continuous at $\text{x}=\text{n}\in\text{Z}$
  • D
    None of these.
✓

Answer

Correct option: B.
Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
$\text{f(x)}=|\cos\text{x}|$
Given function is trigonometric function.
⇒ Hence, it is continuous.
Function is not differentiable at odd multiples of $\frac{\pi}{2}$
⇒ f(x) is not differentiable at $\text{x}=(2+\text{n}+1)\frac{\pi}{2}.$

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