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The number of values of \mathrm{x \in[0,2]} at which the real function \mathrm{f(x)=\left|x-\frac{1}{2}\right|+|x-1|+\tan x}  is not finitely differentiable is

Option: 1

2


Option: 2

3


Option: 3

1


Option: 4

0


Answers (1)

The doubtful points are \mathrm{x=\frac{1}{2}, 1, \frac{\pi}{2}. }

\mathrm{|x-1|}  is differentiable at \mathrm{\frac{1}{2}, \frac{\pi}{2}}  but not differentiable at 1

\mathrm{\left|x-\frac{1}{2}\right|} is differentiable at \mathrm{1, \frac{\pi}{2}}  but not differentiable at \mathrm{\frac{1}{2}}.

Remember \mathrm{|x-a|}  is continuous everywhere, and differentiable everywhere except at \mathrm{x=a}.

\mathrm{\tan x} is differentiable at \mathrm{\frac{1}{2}, 1}  but not differentiable at

\mathrm{\therefore f(x)} is not differentiable at \mathrm{\frac{1}{2}, 1, \frac{\pi}{2}}.

Posted by

Ramraj Saini

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