Quadratic Function

Question

Find algebraically two numbers whose sum is 50 and whose product is a maximum.

Answer 1

x+y = 50

xy = x(50-x) = 50x-x^2 take the derivative & set = 0

50-2x=0

2x=50

x =50/2 = 25

y = 25

xy= 625

It's similar to asking the dimensions of a rectangle that maximizes the area. It's a square

or graphing a hyperbola, xy=a constant, then finding the point on the hyperbola which