Question

Assertion :Let $f\left(x\right)=\int e^x(x-1)(x-2)dx$, then $f\left(x\right)$decreases in the interval (1, 2). Reason: If f(x) is decreasing function then $f^{\prime }\left(x\right)<0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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