SOLUTION: Find the area of the largest rectangle that has two sides on the positive x-axis and the positive y-axis one vertex at the origin and one vertex on the curve y = e^(-x) Please

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Question 999606: Find the area of the largest rectangle that has two sides on the positive x-axis and the positive y-axis one vertex at the origin and one vertex on the curve y = e^(-x)
Please explain
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the rectangle would then be,
A%28x%29=x%2Ae%5E%28-x%29
To find the maximum area, differentiate the area with respect to x.
dA%2Fdx=x%2A%28-e%5E%28-x%29%29%2Be%5E%28-x%29%2A1
dA%2Fdx=e%5E%28-x%29%281-x%29
Set the derivative equal to zero.
e%5E%28-x%29%281-x%29=0
So the solution is,
1-x=0
x=1
So the maximum area of the rectangle is,
A%5Bmax%5D=1%28e%5E%28-1%29%29
A%5Bmax%5D=1%2Fe