Friday, 19 October 2018

calculus - Construct a function which is continuous in [1,5] but not differentiable at 2,3,4





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: |x2|+|x3|+|x4| is continuous (why?) and differentiable everywhere except at 2, 3, and 4.



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