Calculus: derivatives
you are designing a rectangular poster to contain 50 inches squared of printing with a 4 inch margin at the top and bottom; and a 2 inch margin at each side. what overall dimensions will minimize the amount of paper used?

(x − 8)(y − 4) = 50, so y = 4 + 50 x−8 . Then A(x) = x 4 + 50 x − 8 
x > 8. A 0 (x) = 4 − 400 (x − 8)2 , so A 0 (x) = 0 gives x = 18.
 A 00(x) = 800 (x − 8)3 > 0
so the function is concave up, so x = 18 is the absolute minimum. When x = 18, y = 9.