x + y = 42
y = 42 - x
Minimize xy
Miniminize x(42-x)
Minimize -x^2 + 42x
It's an upside-down parabola. You can see the graph here ( https://www.google.com/?gws_rd=ssl#q=plot(-x%5E2+%2B+42x) ).
See how the parabola keeps going down forever on the left and right, forever? That means there is no minimum for -x^2 + 42x, which means there is no minimum for xy.
Example: x = -1, y = +43, xy = -43
Example: x = -1000, y = +1042, xy = -1042000
Example: x = -1000000, y = +1000042, xy = -1000042000000
Answers:
Equation: x + y = 42
Equation: x * y = ? (minimize)
Minimum Product: No minimum exists.
