Find two numbers whose product is 64, and whose sum is a minimim

XY = 64 X + Y = minimum. Substituting X + 64/X = minimum To find the minimum (or maximum), differentiate with respect to X and set the result to zero. Therefore If you want the sum to be a minimum then you must select X=-8, Y=-8 p. s ... But, since the problem specified positive numbers, you select X=8 and Y=8