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Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiability1 Mark
Question
The function$\text{f(x)}=1+|\cos\text{x}|$ is:
  1. Continuous no where.
  2. Continuous everywhere.
  3. Not differentiable at x = 0
  4. Not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$
✓

Answer

  1. Continuous everywhere.

Solution:

Graph of the function $\text{f(x)}=1+|\cos\text{x}|$ is as show blow:

From the graph, we can see that f(x) is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$

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