question_answer

Consider the function, \[f(x)=\left| x-2 \right|+\left| x-5 \right|,x\in R\]. Statement-1: \[f'(4)=0\] Statement-2: \[f\] is continuous in [2, 5], differentiable in (2, 5) and \[f(2)=f(5)\].   AIEEE  Solved  Paper-2012

A) Statement-1 is false, Statement-2 is true.

B) Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.

C) Statement-1 is true, statement-2 is true; statement-2 is not a corect explanation for Statement-1.

D) Statement-1 is true, statement-2 is false.

Correct Answer: C

Solution :

             \[f(x)=3\]                                \[2\le x\le 5\]              \[f'(x)=0\]               \[2<x<5\] \[f'(4)=0\]