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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first number be X.
The second number will be 12-X since the sum of the first and second is 12.
Define the product of the two numbers,
P%28X%29=X%2812-X%29
So to find the extrema, put P%28X%29 into vertex form,
P%28X%29=12X-X%5E2
P%28X%29=-X%5E2%2B12X
P%28X%29=-%28X%5E2-12X%2B36%29%2B36
P%28X%29=-%28X-6%29%5E2%2B36
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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