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

Question

linktra · Answer

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

linktra · Answer

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

steve816 · Answer

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

linktra · Answer

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

linktra · Answer

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

eliesaab · Answer

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

steve816 · Answer

Thanks everyone.

linktra · Answer

your very welcome. ;)