Which one of the following isnot true always?

Options

A. if f(x) is not continuous at x=a, then it is not differentiable at x=a
B. if f(x) is continuous at x=a, then it is differentiable at x=a
C. if f(x) and g(x) are differentiable at x=a, then f(x)+g(x) is also differentiable at x=a
D. if a function f(x) is continuous at x=a, then `underset(atoa)(lim)f(x)` exists

Answer

B

Explanation

It a function f(x) is continuous at x=a, then it may or may not be differentiable at x=a.