The region R is a rectangle with vertices P(a,lna), Q(a,0), S(3,0), and T(3,lna), where 1<a<3.

Question

A.) Write an expression that gives the area of the rectangle as a function of a.
B.) The area of the rectangle is maximized for some c beween 1 and 3. Write the expression you would need to solve in order to find c.

Answer 1

Working this through a little more, I believe that the expression for A should be f(a) = (ln(a))(3-a). Now, I just need help with part B. I am really no good when it comes to maximization, so I could really use some help.