Consider the function $f(x) = |x-2| + |x-5|, x \in R$. <br> Statement 1: $f'(4) = 0$ <br> Statement 2 : $f$ is continuous in [2, 5], differentiable in (2, 5) and $f(2) = f(5)$.

Question

( A ) Statement 1 is false, statement 2 is true
( B ) Statement 1 is true, statement 2 is false
( C ) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
( D ) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1