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does there exist a function which is continuous everywhere but not differentiable at exactly two points? justify your answer.

does there exist a function which is continuous everywhere but not differentiable at exactly two points? justify your answer.
 
 

Grade:12

1 Answers

Vikas TU
14149 Points
7 years ago
Yes,
Take f(x) = |x-1| + |x-2|
For case 1. when x
f(x) = -x+1 – x + 2 = -2x + 3
 
case 2. when x > = 2
f(x) = x-1+x-2
     = 2x – 3
 
case 3
when  1
f(x) = x – 1 – x +2
     = 1
 
Draw the graph for this given interval and U will come to know that it is continuos and non – differentaible at exactly two point.
 
Like this there can be number of modulus function U can think.

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