Question

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. $(2,+\infty )$

Answer 1

Answer: (C)

$f\left(x\right)=\int e^x\left(x-1\right)\left(x-2\right)dx$
For decreasing function $,f^{\prime }\left(x\right)<0$
$\Rightarrow e^x\left(x-1\right)\left(x-2\right)<0\Rightarrow \left(x-1\right)\left(x-2\right)<0$
$\Rightarrow 1<x<2,\because e^x>0\forall x\in R$