Rationalised 2023-24
PROOFS IN MATHEMATICS
195
Example 9 Every continuous function is differentiable 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