Q. Roll’s theorem is not applicable to the function $f(x) = |x|$ for $- 2 \leq x \leq 2$ because
A) $f$ is continuous for $- 2 \leq x \leq 2$
B) $f$ is not derivable for $x = 0$
C) $f( - 2) = f(2)$
D) $f$ is not a constant function
Explanation
(b)
Since, $f(x) - |x|,\ \forall - 2 \leq x \leq 2$
$= \left\{ \begin{array}{r}
- x,\ \ \ \forall - 2 \leq x < 0 \\
x,\ \ \ \ \forall\ 0 \leq x \leq 2
\end{array} \right.\$
This function is not derivable at $x = 0$, therefore Rolle’s theorem is not applicable
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.