SOLUTION: the difference of two numbers is 24. Find the two numbers if their product is to be a minimum.

x - y = 24,
xy  ---->  min.


It is the same as to find the minimum of the quadratic function x*(x-24), or, which is the same, of the quadratic function .


The roots of the function are at 0 and 24; therefore, the minimum is at  the middle point  x =  = 12.

Then y = 12-24 = -12.