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?

amistre64 · Answer

well, how DID you come up with it?

amistre64 · Answer

x+y = 12 ; y = 12-x

xy = max

x(12-x) = max

12x - x^2 = max at its vertex

amistre64 · Answer

whose difference is 12 ... i gotta get better glasses

amistre64 · Answer

x-y = 12 ; y = x-12

xy = max

x(x-12) = max

x^2 - 12x = max  at infinity

anonymous · Answer

i repeat, maybe it means two numbers whose sum is 12
if the difference is 12 i can make it as large as possible

anonymous · Answer

100,112
100000, 100012 etc

amistre64 · Answer

id do sum too :)

anonymous · Answer

I have no idea!

anonymous · Answer

i am going to bet it means two numbers that add to 12 not "whose difference is 12"

anonymous · Answer

the answer is (0,9)
it's at the back of the book, but how????

amistre64 · Answer

9*0 = 0 not 12

anonymous · Answer

ok now we really have a problem because it is not the case that the difference or the sum of 0 and 9 is 12!!

amistre64 · Answer

theres a valid thought in there someplace lol

anonymous · Answer

either there was a typo in the book or this is the answer to a different problem
0 + 9 = 9, 9 - 0 = 9, there is no 12 to be had here

anonymous · Answer

I'm sorry, it's a wrong question
the answer is + and - 6

anonymous · Answer

produce is a minimum maybe ??

anonymous · Answer

Itr makes sence now, but in my formula it is just 6, where do we get the - 6?

anonymous · Answer

nope, says max

anonymous · Answer

now way that 
$$6\times -6=-
36$$ is a maximum

anonymous · Answer

#no way

anonymous · Answer

but even if it say minimum ( there is similar question in the book but with min), how the heck we will get -6 and +6?

anonymous · Answer

what about 100 and 112
the difference is 6 and the product is much bigger than -36

anonymous · Answer

This question drives me nuts lol

anonymous · Answer

i can see why because it makes no sense at all

anonymous · Answer

minimum represents the direction of the porabola ( opens up )

anonymous · Answer

we don't really care about it

anonymous · Answer

we can solve this problem 
find two numbers whose sum is 12 and whose product is a maximum

anonymous · Answer

I don't knwo....

anonymous · Answer

sorry

anonymous · Answer

That's fine. I'll ask the teacher