Consider the function $f(x)=|x-2|+|x-5|\;x\in R$.

Question

Statement- 1: $f'(4)=0$

Statement- 2: $f$ is continuous in [2,5] differentiable in (2,5) and $f(2)=f(5)$

$\begin{array}{1 1}(a)\;\text{Statement-1 is false,Statement-2 is true}\\(b)\;\text{Statement-1 is true,Statement-2 is true,Statement-2 is a correct explanation for Statement-1}\\(c)\;\text{Statement-1 is true,Statement-2 is true,Statement-2 is not a correct explanation for Statement-1}\\(d)\;\text{Statement-1 is true,Statement-2 is false}\end{array}$