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A printed poster is to have a total area of 742 square inches with top and bottom margins of 6 inches and side margins of 5 inches. What should be the dimensions of the poster so that the printed area be as large as possible? To solve this problem let a denote the width of the poster in inches and let y denote the length in inches. We need to maximize the following function of a and y: We can reexpress this as the following function of x alone: f ( ac ) = 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"(a) 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