Math Is Fun Forum

John92

Guest

Stuck trying to prove/show something

Hey guys, i'm doing an econ assignment but i'm either going about the question in completely the wrong way - or im stuck on some math that i'm unable to do. Assuming it's the second (because i dont just want to post the question and get you to do the whole thing for me), here's what im stuck on.

A = 9xy

B = 9x + 9y - 18xy

C = 9 - 9x - 9y + 9xy

D = 12xy - 6x - 6y + 6

I want to prove that there are no values of x and y (where x and y are both values between 0 and 1) for which D is the greatest.

Is that possible to do numerically? Only thing i can think of is having some software plot a 3d graph and show that the D surface is always below at least one other - obviously thats no good for helping me do my homework though lol.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck trying to prove/show something

Hi;

D surface is always below at least one other

I am not following you here. Please post the exact question. Wording is very important in mathematics.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John92

Guest

Re: Stuck trying to prove/show something

Sorry, maybe ignore that bit, i'm not sure that even makes sense anyway - i was just speculating about how i'd demonstrate that at least one of the values, A, B, C would be greater than D at every value of x and y.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck trying to prove/show something

If x,y were in the interval of 0 and 1?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John92

Guest

Re: Stuck trying to prove/show something

That's right

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck trying to prove/show something

Hi;

A is out, it is not always greater than D in the closed interval (0,1).

B is out, it is not always greater than D in the closed interval (0,1).

C is out, it is not always greater than D in the closed interval (0,1).

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Stuck trying to prove/show something

I don't think the point is to prove that one of those is always greater than D, but rather at least one of those will be greater than D for some x and y.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck trying to prove/show something

Hi;

that at least one of the values, A, B, C would be greater than D at every value of x and y

Looks like he is saying A or B or C is always greater in that interval.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.