Chapter 4.7, Problem 46E

Area Perform the following steps to find the maximum area of the rectangle shown in the figure.

(a) Solve for c in the equation $f(c)=f(c+x)$.

(b) Use the result in part (a) to write the area A as a function of x. [Hint: $A=xf(c)$ ]

(c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions of the rectangle of maximum area. Determine the required area.

(d) Use a graphing utility to graph the expression for c found in part (a). Use the graph to approximate

$\underset{x\to 0^{+}}{\lim }c$ and $\underset{x\to 0}{\lim }c$.

Use this result to describe the changes in the dimensions and position of the rectangle for $0<x<\infty$.