Question 999606
The area of the rectangle would then be,
{{{A(x)=x*e^(-x)}}}
To find the maximum area, differentiate the area with respect to x.
{{{dA/dx=x*(-e^(-x))+e^(-x)*1}}}
{{{dA/dx=e^(-x)(1-x)}}}
Set the derivative equal to zero.
{{{e^(-x)(1-x)=0}}}
So the solution is,
{{{1-x=0}}}
{{{x=1}}}
So the maximum area of the rectangle is,
{{{A[max]=1(e^(-1))}}}
{{{A[max]=1/e}}}