Find two numbers whose difference is 168 and whose product is a minimum

If x - Q = 100, then Q = 100 + x

Substitute this into the following equation:

F(x) = x*Q <this is the eqation for which you want to find a minimum

F(x) = x *(100 + x)

F(x) = x^2 + 100x

Graph that equation, and look for its lowest point. The lowest point is at x = -50, f(x) = -2500

Since Q = 100 + x, then Q = 100 + (-50) = 50

50 - (-50) = 100, and the product--being -2500--is a minimum.