Q

# The interval in which y = x2 e–x is increasing is

19) The interval in which $y = x ^2 e ^{-x}$is increasing is

(A) $( - \infty , \infty )$ (B) $( - 2 , 0 )$(C) $( - 2 , \infty )$ (D) $( 0, 2 )$

Views

Given function is,
$f(x) \Rightarrow y = x ^2 e ^{-x}$
$f^{'}(x) \Rightarrow \frac{dy}{dx} = 2x e ^{-x} + -e^{-x}(x^{2})$
$xe ^{-x}(2 -x)$
$f^{'}(x) = xe ^{-x}(2 -x)$
Now, it is clear that $f^{'}(x) > 0$  only in the interval (0,2)
So,  $f(x) \Rightarrow y = x ^2 e ^{-x}$ is  an increasing function for the interval  (0,2)