Q. Let $f:R \rightarrow R$ be a function defined by$f(x) = \min{\{ x + 1,\ |x| + 1\}}$. Then, which of the following is true?
A) $f(x) \geq 1$ for all $x \in R$
B) $f(x)$ is not differentiable at $x = 1$
C) $f(x)$ is differentiable everywhere
D) $f(x)$ is not differentiable at $x = 0$
Explanation
(c)
It is clear from the graph that minimum $f(x)$ is
[image:5_image4.emf]
$f(x) = x + 1,\ \ \forall\ x \in R$
Hence, it is a straight line, so it is differentiable everywhere
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.