若兩個數之和是16,求它們的積的極大值

x+y=16
y=16-x

Product = xy = x(16-x) = 16x-x^2.  Rewriting in the form ax^2+bx+c gives a=-1, b=16.

Turning point is at (-b/2a, f(-b/2a)) = (8, 64).  Checking that it is a maximum, the answer is 64.