SOLUTION: One number subtracted from another is 11. The product of the two numbers is a minimum. What are the numbers?

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Question 819516: One number subtracted from another is 11. The product of the two numbers is a minimum. What are the numbers?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Let p = the product of the two numbers, x and y.
y-x=11 and xy=p
p=x%2A%28x%2B11%29=x%5E2%2B11x
A parabola with a minimum. Looking back at the factored form for p, roots are at x=0 and x=-11.
The minimum occurs exactly in the middle, for highlight%28x=-11%261%2F2%29; find also that y=11%2B%28-5%261%2F2%29=highlight%285%261%2F2=y%29