Engineering Board Exam Reviewer · Curve Analysis: Critical Points, Concavity, and Inflection · medium

Find the maximum value of f(x)=xe-x for x≥0.

1. 0.37
2. 1
3. 0.5
4. 2.72

Answer

A. 0.37

Solution

f'(x)=e-x(1-x)=0 x=1, and f' changes from positive to negative. The maximum is f(1)=e-1 0.37.

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