Question 2(d)

Question

A rectangle has one vertex at \((0,0)\) and the opposite vertex on the curve \(y=6e^{1-0.5x}\), where \(x>0\), as shown below.

Find the maximum possible area of the rectangle.

You must use calculus and show any derivatives that you need when solving this problem.

You do not have to prove that the area you have found is a maximum.

Try the question yourself first. If you get stuck, open the hints before using the full walkthrough.