The number of points at which the function $f(x)=\max \{a-x, a+x, b\},-\infty < x < \infty$ $0 < a < b$ cannot be differentiable, is

• A

  0
• B

  1
• Correct answer
  C

  2
• D

  3

Solution

Graph of $f(x)$ There are two sharp turns. Hence, $f(x)$ cannot be differentiable at two points.

Hence, the correct answer is option: 'C'.