A) (4. 5)
B) (0,2)
C) (2.3)
D) (3, 4)
Correct Answer: B
Solution :
Given.\[f(x)={{x}^{2}}{{e}^{-x}}\] On differentiating both sides w.r.t.\[x,\]we get. \[f'(x)=2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}\] For\[f(x)\] to be increasing,\[f'(x)>0\] \[\Rightarrow \] \[2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}>0\] \[\Rightarrow \] \[{{e}^{-x}}x(2-x)>0\] \[\therefore \] \[x\in (0,2)\]You need to login to perform this action.
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