Question

Find two numbers whose difference is 100 and whose product is a minimum. Good luck.

Answer 1

Um, those would be -50, and 50 I believe.

Answer 2

Because on a number line they have 100 units between them, and if you add them together you get 0 which is a minimum.

Answer 3

Ok, now let me change the question, how would you find two numbers whose difference is 100 and whose product is a MAXIMUM.

Answer 4

Hm, 2,400 and 2,500? Because they are different by 100 and have the product of 6,000,000.

Answer 5

You could really do this with any 2 high numbers that are 100 units apart.

Answer 6

let
\[
f(x)=x(x+100)=x^2 +100x
\]
This a parabola, it has a minumum at x=-50
hence x+100=50
So the answer -50 and 50

Answer 7

Thanks everyone.

Answer 8

your very welcome. ;)