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Number of points where the function f(x)=max(\left | \tan \: x \right |,\cos \left | x \right |) is non differentiable in the interval (-\pi ,\pi ) is

Option: 1

4


Option: 2

6


Option: 3

3


Option: 4

2


Answers (1)

As we have learnt in

 

Differentiability -

Let  f(x) be a real valued function defined on an open interval (a, b) and  x\epsilon (a, b).Then  the function  f(x) is said to be differentiable at   x_{\circ }   if

\lim_{h\rightarrow 0}\:\frac{f(x_{0}+h)-f(x_{0})}{(x_{0}+h)-x_{0}}


or\:\:\:\lim_{x\rightarrow x_{0}}\:\frac{f(x)-f(x_{0})}{x-x_{0}}

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The functions is not differentiable at two points between  x=-\frac{\pi}{4}\: and\: x=\frac{\pi}{4}

also function is not continuous at x=-\frac{\pi}{2}\: and\: x=\frac{\pi}{2}. hence at four points function is not differentiable.

Posted by

Sumit Saini

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