Chapter 5.4, Problem 80E

(a)

To determine

To calculate: The value of c in the equation $f\left(c\right)=f\left(c+x\right)$

(b)

To determine

To calculate: The Area of the rectangle, A as a function of x.

(c)

To determine

To graph: The Area function and to determine the maximum area of the rectangle.

(d)

To determine

To graph: The function $c=x+e^x$ and approximate the values of $\underset{x\to 0^{+}}{\lim }c$ and $\underset{x\to {\infty }^{+}}{\lim }c$.