Find out that if f is a differentiable function at a, must f be also continuous at a or not?
A continuous function may or may not be differentiable.
Answer: If f(x) is a differentiable function, then it is a continuous function.
A function that is differentiable is always a continuous function.
Given f is a differentiable function.
Consider, lim x → a f(x) - f(a) = lim x → a [(f(x) - f(a))/(x - a)] × x - a
= f'(a) × 0
So, this means lim x → a f(x) = f(a)