
Concept explainers
True or False? Justify the answer with a proof or a counterexample.
367. Every function has a derivative.

To show:Justify whether every function has a derivative or not.
Answer to Problem 367RE
False
Explanation of Solution
Formula Used :The definition of derivative is given by, if
Let us consider the counter example,
Here, f(x) is continuous for all real values of x. But it is not differentiable at x= 0.
Hence, f(x) is not differentiable at x=0.
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