Determine the 2 numbers whose difference is 12 and whose product is a maximum.I came up with (x + 6)^2 - 36

But, what do I do now?

It is functions, grade 11.

Do I need to explain how I got x + 6)^2 - 36?

Question

Determine the 2 numbers whose difference is 12 and whose product is a maximum.I came up with (x + 6)^2 - 36

But, what do I do now?

It is functions, grade 11.

Do I need to explain how I got x + 6)^2 - 36?

anonymous · Answer

put one number as x 
then since the difference is 12 the other is x - 12

anonymous · Answer

or you could use x and x + 12, which is what it looks like you used

anonymous · Answer

although on the face of it i don't see how you can solve this problem.  maybe it means the sum is 12, not the difference

anonymous · Answer

to me "difference" means what you get when you subtract
so the difference between 100 and 112 is 12

anonymous · Answer

That is exactly what I used.
So, then it is
Product =(x)(x+12)
= x^2 + 12x
= x^2 +12x + 36 - 36
=  (x + 6)^2 - 36

I did this because that's what we are doing now
I'm not sure how from that I'm finding these 2 numbers