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Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferentiability1 Mark
Question
The function $\text{f(x)}=|\cos\text{x}|$ is:
  1. Differentiable at$\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  2. Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  3. Neither differentiable nor continuous at $\text{x}=\text{n}\in\text{Z}$
  4. None of these.
✓

Answer

  1. Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
Solution:
$\text{f(x)}=|\cos\text{x}|$
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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