SOLUTION: i am thinking of 2 numbers. The difference between them is 12. What is the smallest product (multiplication) I can get with my two numbers? Hint: it is not zero! Create a function

Question 1029384: i am thinking of 2 numbers. The difference between them is 12. What is the smallest product (multiplication) I can get with my two numbers? Hint: it is not zero! Create a function you can graph. What part of the graph would we call "smallest"?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the first number be .
The second number will be since the sum of the first and second is 12.
Define the product of the two numbers,

So to find the extrema, put into vertex form,

So what that tells you is that the maximum product of the two numbers is 36 (occurring when X=6) and the parabola opens downward so it's unbounded in the negative direction.
So there is no minimum value for this function, only a maximum.
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