Proof  We consider some functions given by
(i)
f (x) = x2
(ii)
g(x) = ex
(iii)
h(x) = sin x
These functions are continuous for all values of x If we check for their
differentiability, we find that they are all differentiable for all the values of x This
makes us to believe that the generalisation “Every continuous function is differentiable”
may be true But if we check the differentiability of the function given by “φ(x) = | x|”
which is continuous, we find that it is not differentiable at x = 0