find a function describing the maximum area

Question

You have a rectangle in the first quadrant, in the xy-plane. one corner is at the origin, one on the x-axis, one on the y-axis and the last one on the graph of f(x)=3e^-x.Find a function describing the area of the rectangle. use the function to maximize the area of the rectangle

Answer 1

Area = 3xe^-x

A' = -3xe^-x+ 3e^-x=0

3e^-x(-x+1) =0

-x+1=0

x=1

max Area = 3/e= about 1.1036