Calculus
posted by Anonymous .
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.
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.

Working this through a little more, I believe that the expression for A should be f(a) = (ln(a))(3a). 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.
Respond to this Question
Similar Questions

geometry
The height of triangle ACE is 12 and base AE=20. A rectangle is inscribed in triangle ACE as shown in the diagram a) express the rectangle's area as a function of x and y b)Use the fact that triangle ACE is similar to BCD to write … 
Math
If the length of a rectangle is (2x1)cm and its width is (x+3)cm. How do i write an expression in the form ax^2+bx+c for the area of the rectangle? 
Algebra I
Rectangle ABCD has vertices C and d on the xaxis and vertices A and B on part of the parabola y = 9  x^2 that is above the xaxis. a.) Find the coordinates of A, B, C, and D in terms of x. b.) Determine the Area of the rectangle … 
9th grade polynomials
How do you write the expression for the area of the rectangle If the length of a rectangle is two more than three times it's width,then write an expression for area of the rectangle Find the perimeter of the rectangle in problem 1. 
calculus
A rectangle is bounded by the xaxis and the semicircle y = ¡Ì36 ¨C x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. 
CALCULUS
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. I found that the expression for the area of the rectangle is f(a) = (ln(a))(3a). The area of the rectangle is maximized for some … 
Math
The first question is this: Helen designs a rectangle with an area of 225 square units. Her rectangle is the largest rectangle (that is, with largest area) with wholenumber side lengths that can be made from the perimeter of the rectangle. … 
Math
A rectangle is inscribed in a semi circle of radius 2, let x represent half the length of the rectangle. Write an expression for the area of the rectangle in terms of x. Well I know area=length X width. That's about all I know what … 
Algebra
Top of the rectangle is 2x+5 right hand side is 5. Write an expression for the area of the rectangle. Then find the area of the rectangle in square feet if x=3. Then I need to find the value of x if the area of the rectangle is 1y0 … 
Algebra
A rectangle has dimensions in feet as shown in the figure it is 2x +5 And one side is 8. I need to write an expression for the area of the rectangle. B. Find the area of the rectangle, in sq.ft. if x=3 C. Find the value of x if the …