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Question

Select the correct statement fiven option for the function f(x)=xe1-x


A

Strictly increases in the interval 12,2

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B

Increases in the interval 0,

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C

Decreases in the interval 0,2

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D

Strictly decreases in the interval (1,)

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Solution

The correct option is D

Strictly decreases in the interval (1,)


Finding the derivative of the given function and finding the interval:

f(x)=xe1-x

Differentiating the given function

f'(x)=xe1-x+e1-x=e1-x(1-x)

f'(x)<0,(1,)

f(x)strictly decreases in the interval (1,)

Therefore, the correct answer is option (D).


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