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Select the correct statement from a., b., c., d.. The function `f(X)=xe^(1-x)`

A

strictly increase in the inverval `(1/2,2)`

B

increases in the interval `(0,oo)`

C

decreases in the interval `(0,2)`

D

strictly decreases in the interval `(1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `f(x)=xe^(1-x)`
`impliesf'(x)=-e^(1-x)+e^(1-x)=e^(1-x)(1-x)`
`impliesf'(x)lt0, AA(1,oo)`
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