A) \[(0,2)\]
B) \[(2,3)\]
C) \[(3,4)\]
D) \[(4,5)\]
Correct Answer: A
Solution :
Given, \[f(x)={{x}^{2}}{{e}^{-x}}\] \[\Rightarrow \] \[f'(x)=2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}\] For \[f(x)\] to be increasing, \[f'(x)>0\] \[\Rightarrow \] \[2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}>0\] \[\Rightarrow \] \[{{e}^{-x}}(2x-{{x}^{2}})>0\] \[\Rightarrow \] \[x(2-x)>0\] \[\Rightarrow \] \[x\in (0,2)\]You need to login to perform this action.
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