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  • Help me answer: - Letbe a function defined by . If K be the set of all points at whichis not differentiable, then - Limit , continuity and differentiability - JEE Main

Let f:(-1,1)\rightarrow R be a function defined by f(x) = \textup{max}\left\{-|x|, - \sqrt{1-x^2} \right \} . If K be the set of all points at which f is not differentiable, then K has exactly:

  • Option 1)

    two elements

  • Option 2)

    three elements 

  • Option 3)

    five elements 

  • Option 4)

    one element

Answers (1)

best_answer

 

Properties of differentiable functions -

At every corner point  f(x) is continuous but not differentiable.

ex:    | x - a |  is continuous but not differentiable at  x = a  for  a > 0 

- wherein

 

 

Condition for differentiability -

A function  f(x) is said to be differentiable at  x=x_{\circ }  if   Rf'(x_{\circ })\:\:and\:\:Lf'(x_{\circ })   both exist and are equal otherwise non differentiable

-

f:(-1,1)\rightarrow R

f(x)=max\left \{ \right.{-\left | x \right |,\sqrt{1-x^{2}}}\left. \right \}

Plot the graph

Non-differentiable at 3 points in ( -1, 1 ).

 

 


Option 1)

two elements

Option 2)

three elements 

Option 3)

five elements 

Option 4)

one element

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