The points of non differentiability of $f(x) =|x-2|+|x-3|$

A. 1

B. 2

C. 3

D. 4

E. 5

Choose the correct answer from the options given below :

B and C only

The correct answer is Option (2) → B and C only

$f(x) =|x-2|+|x-3|=\left\{\begin{matrix}2x-5,&x>3\\1,&2≤x≤3\\-2x+5,&x<2\end{matrix}\right.$

so $f'(x)=\left\{\begin{matrix}2,&x>3\\0,&2<x<3\\-2,&x<2\end{matrix}\right.$

so $\lim\limits_{x→2^+}f'(x)=2≠0=\lim\limits_{x→3^-}f'(x)$

$\lim\limits_{x→2^+}f'(x)=0≠-2=\lim\limits_{x→2^-}f'(x)$

point of non differentiability → 2, 3