Q. Which one of the following is not true always?
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 $\lim_{x \rightarrow a}{f(x)}$ exists
Explanation
(b)
If a function $f(x)$ is continuous at $x = a$, then it may or may not be differentiable at $x = a$
$\therefore$ Option (b) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.