Q. The differential coefficient of the function $|x - 1| + |x - 3|$ at the point $x = 2\$is
A) $- 2$
B) 0
C) 2
D) undefined
Explanation
(b)
Let $f(x) = |x - 1| + |x - 3|$
$f(x) = \left\{ \begin{matrix}
- (x - 1) - (x - 3), & x < 1 \\
(x - 1) - (x - 3), & 1 \leq x < 3 \\
(x - 1) + (x - 3), & x \geq 3
\end{matrix} \right.\$
$f(x) = \left\{ \begin{matrix}
4 - 2x, & x < 1 \\
2, & 1 \leq x < 3 \\
2x - 4, & x \geq 3
\end{matrix} \right.\$
At $x = 2$,
$f(x) = 2 \Rightarrow f^{'}(x) = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.