A printed poster is to have a total area of 580 square inches with top and bottom margins of 3 inches and side margins of 4 inches. What should be the dimensions of the poster so that the printed area be as large as possible?

To solve this problem let $x$ denote the width of the poster in inches and let $y$ denote the length in inches. We need to maximize the following function of $x$ and $y$:

We can reexpress this as the following function of $x$ alone:
$f(x) =$
We find that $f(x)$ has a critical number at $x=$
To verify that $f(x)$ has a maximum at this critical number we compute the second derivative $f''(x)$ and find that its value at the critical number is , a negative number.
Thus the optimal dimensions of the poster are inches in width and inches in height giving us a maximumal printed area of square inches.