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Question

Let f(x)=xex1-x, then f(x) is:


A

increasing on -12,1

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B

Decreasing on R

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C

Increasing on R

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D

decreasing on -12,1

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Solution

The correct option is A

increasing on -12,1


Explanation for the correct option:

Given that: f(x)=xex1-x

Differentiating the expression with respect to x:

f(x)=xex1-xf'(x)=xex1-x.x(-1)+(1-x)+ex1-xf'(x)=ex1-xx(1-2x)+1f'(x)=ex1-x-2x2+x+1f'(x)=-ex1-xx-1(2x+1

We know that: f(x) is increasing when f'(x)<0 and decreasing when f'(x)>0.

Therefore, in this case, f(x) is increasing in -12,1.

Hence, the correct Option is (A).


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