Q. Let$f(x) = \int_{}^{}e^{x}(x - 1)(x - 2)dx$. Then, $f$ decreases in the interval
A) $( - \infty,\ - 2)$
B) $( - 2,\ - 1)$
C) $(1,\ 2)$
D) $(2,\ \infty)$
Explanation
(c)
Given that, $f(x) = \int_{}^{}{e^{x}(x - 1)(x - 2)dx}$
On differentiating w.r.t. $x$, we get
$f^{''}(x) = e^{x}(x - 1)(x - 2)$
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Since, $f(x)$ is decreasing
$\therefore\ \ f^{''}(x) < 0\ \ \Rightarrow \ \ e^{x}(x - 1)(x - 2) < 0$
$\Rightarrow (x - 1)(x - 2) < 0\ \ \ \Rightarrow \ \ 1 < x < 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.