Among all pairs of numbers whose difference is 10, find a pair whose product is as small as possible. What is the minimum product? a. the pairs of numbers whose difference is 10 and whose product is as small as possible is___ b. The minimum product is___

Question

anonymous · Answer

$(10,0)$

Answer b yourself.

anonymous · Answer

hmm what about -5 and 5?

anonymous · Answer

Hm. That may very well be the best pair. Do you have a proof?

anonymous · Answer

ok that was wrong
but idea was right

anonymous · Answer

try with $x$ and $x-10$

anonymous · Answer

Hm. So $x-y=10$, $y=x-10$, and $xy=x(x-10)=x^2-10x$. The minima of $x^2-10x$ is at $x=5$, so $x=5$, $y=5-10=-5$.

Nice job.