a rectangle is inscribed under the curve y=e^(-x)^2, with its base along the x-axis. Find the rectangle of largest area, subject to the restriction that the base does not exceed 4 units.

Now I want to maximize the area of the rectangle, so should I do this?

A=xy

=[e^(-x)^2]x

Tested the domain

f(0)=1

f(4)=0.0000000112

now this doesn't make much sense because we dont have a rectangle if the largest area is 1..... x =0? not rectangle.

Please guide me to enlightenment! really appreciate it. thank you