Q. The function $f(x) = \max{\lbrack(1 - x),\ (1 + x),\ 2\rbrack}$, $x \in ( - \infty,\ \infty)$ is
A) Continuous at all points
B) Differentiable at all points
C) Differentiable at all points except at $x = 1$ and $x = - 1$
D) None of the above
Explanation
(c)
[image:5_image3.emf]
It is clear from the graph that $f(x)$ is continuous everywhere and also differentiable everywhere except $\{ - 1,\ 1\}$ due to sharp edge
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.