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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
Question
Let $\text{f(x)}=|\sin\text{x}|.$ then,
  1. f(x) is everywhere differentiable.
  2. f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
  3. f(x)  is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
  4. None of these.
✓

Answer

  1. f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$

Solution:

$\text{f(x)}=|\sin\text{x}|$

Given function is continuous and differentiable on $(2\text{n}\pi,(2\text{n}+1)\pi)$

But not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$

As $\sin\text{n}\pi=0$ for $\text{n}\in\text{Z}.$

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