Question

The interval in which the function $x^{2}e^{- x}$ is non decreasing, is

• A. $( - \infty,2\rbrack$
• B. [0, 2]
• C. $\lbrack 2,\infty)$
• D. None of these

Answer 1

Answer: (B)

$0, 2$

Answer 2

Let $f(x) = x^{2}e^{- x}$

⇒ $\frac{dy}{dx} = 2xe^{- x} - x^{2}e^{- x} = e^{- x}(2x - x^{2})$

Hence $f^{'}(x) \geq 0$ for every$x \in \lbrack 0,2\rbrack$,

therefore it is non-decreasing in [0, 2].