Consider the function, $f(x)=|x-2|+|x-5|, x \in R$ Statement $1: f^{\prime}(4)=0$ Statement $2: f$ i

Question

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 $f(2)=f(5)$.

Professor PC Thomas Classes · Answer

(a) : $f(x)=|x-2|+|x-5|$\ $\Rightarrow f(x)=\left\{\begin{array}{cc}7-2 x, & x<2 \ 3, & 2 \leq x \leq 5 \ 2 x-7, & x>5\end{array}ight.$\ Statement-1 : $f^{\prime}(4)=0$. True\ Statement-2 : $f$ is continuous in $[2,5]$, differentiable in $(2,5)$ and $f(2)=f(5)$. True\ But Statement 2 is not a correct explanation for Statement 1.\