Q58 / 90 · JEE Main 2012 (Offline) · Mathematics

Consider the function $f(x)=|x-2|+|x-5|, x \in R$. Statement $1$: $f^{\prime}(4)=0$ Statement $2$: $f$ is continuous in $[2,5]$, differentiable in $(2,5)$ and $f(2)=f(5)$.

  • A
    Statement $1$ is false, statement $2$ is true
  • Correct answer
    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 correct explanation for statement $1$
  • D
    Statement $1$ is true, statement $2$ is false

Solution

$f(x) =7-2 x ; x < 2$ $=3$ ; $\quad2 \leq x \leq 5$ $=2 x-7 ; x>5$ $f(x)$ is constant function in $[2,5]$ $f$ is continuous in $[2,5]$ and differentiable in $(2,5)$ and $f(2)=f(5)$ by Rolle's theorem $f^{\prime}(4)=0$ $\therefore$ Statement $2$ and statement $1$ both are true and statement $2$ is correct explanation for statement $1$.

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

Relevant Questions