Construct a function which is continuous in [1,5] but not differentiable at 2,3,4.
This question is just after the definition of differentiation and the theorem that if f is finitely derivable at c, then f is also continuous at c. Please help, my textbook does not have the answer.
Answer
|x| is continuous, and differentiable everywhere except at 0. Can you see why?
From this we can build up the functions you need: |x−2|+|x−3|+|x−4| is continuous (why?) and differentiable everywhere except at 2, 3, and 4.
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