Q. A function $f$ is defined by $f(x) = e^{x}\sin x$ in$\lbrack 0,\ \pi\rbrack$. Which of the following is not correct?
A) $f$ is continous in $\lbrack 0,\ \pi\rbrack$
B) $f$ is differentiable in $\lbrack 0,\ \pi\rbrack$
C) $f(0) = f(\pi)$
D) Rolle’s theorem is not true in $\lbrack 0,\ \pi\rbrack$
Explanation
(d)
Given, $f(x) = e^{x}\sin{x,\ \ \ x \in \lbrack 0,\ \pi\rbrack}$
At $x = 0,\ \ \ \ f(0) = 0$
And at $x = \pi,\ \ \ f(\pi) = 0$
Also, it is continuous and differentiable in the given interval.
Hence, it satisfies the Rolle’s theorem.
Hence, option (d) is the required answer
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.