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Does there exist a function which is continuous everywhere,but not differentiable at two points? Justify

Does there exist a function which is continuous everywhere,but not differentiable at two points?
Justify

Grade:10

3 Answers

Ajay
209 Points
5 years ago
y\quad =\quad x\quad if\quad x<=1\\ \quad y\quad =\quad 1\quad if\quad 1<x<=2\\ \quad y\quad \quad =\quad x-1\quad if\quad x>2
 
The above function is continous everywhere but not differentaible at 1 and 2.
If you draw graph, it has pointed edges at 1 and 2 which indicates it is not differentaible at these points
Nandana
110 Points
4 years ago
hi,
  for your question , there are so many functions involving quadratic equations & one of the fundamentals functions are sinsoidal signals like sin & cos
      
    take mod (cos x ) from 0 to 270 , it is continuous everywhere but it is not differentiable at 90 & 270 .
 
                                          thank you
Anusha
11 Points
4 years ago
F(x)=min{x,x^2},for every real value of xAnswer:if u draw the graph of the above function the graph has two sharp edges ,at these points the function is not differentiable

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