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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives

Find the interval in which $ y=x^2e^{-x}$ is increasing.

1 Answer

Toolbox:
  • For increasing $ f ' (x) \geq 0$
  • For decreasing $ f ' (x) \leq 0$
Step 1
$ \large\frac{dy}{dx} = 2x\: e^{-x}-x^2e^{-x}=0$
$ \Rightarrow x = 0, \: 2$
$ f(x)$ is increasing in [ 0 2 ]
in $ ( -\infty, \: 0]\: \cup \: [2\: \infty)\: f(x)$ is decreasing
answered Apr 13, 2013 by thanvigandhi_1
 
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