Question

Which one of the following is not true always ?

• A. If a function $f(x)$ is continuous at $x = a$ , then $\lim_{x \to a} f{(x)}$ exists
• B. If $f(x)$ and $g(x)$ are differentiable at $x = a$, then $f(x) + g(x)$ is also differentiable at $x = a$
• C. If $f (x)$ is continuous at $x = a$, then it is differentiable at $x = a$
• D. If $f(x)$ is not continuous at $x = a$, then it is not differentiable at $x = a$

Answer 1

Answer: (C)

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