Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

max. value

benice

Member

Registered: 2010-06-10

Posts: 117

Website

Re: max. value

Consider points A(0,1), B(3,4), C(0,0), D(1,0), P(x,y).
We have
|f(x,y)|
= |d(P,A) + d(P,B) - d(P,C) - d(P,D)|
= |d(P,A) - d(P,C) + d(P,B) - d(P,D)|
≤ |d(P,A) - d(P,C)| + |d(P,B) - d(P,D)|
≤ d(A,C) + d(B,D)
= 1 + sqrt(20)
= 1 + 2 sqrt(5) ...... Ans.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: max. value

Hi benice;

What does d(P,A) do? Can you post it?

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: max. value

hi bobbym,

I think it's just an abbreviation for the distance between the points.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: max. value

Thanks benice you are Right.

But can you explain me Why we take {d(P,A) - d(P,C)} + {d(P,B) - d(P,D)}

We also take {d(P,A) - d(P,D)} + {d(P,B) - d(P,C)}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: max. value

Hi

I think it's just an abbreviation for the distance between the points.

Thanks Bob, that is what it does look like.

---

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.

benice

Member

Registered: 2010-06-10

Posts: 117

Website

Re: max. value

Thanks benice you are Right.

But can you explain me Why we take {d(P,A) - d(P,C)} + {d(P,B) - d(P,D)}

We also take {d(P,A) - d(P,D)} + {d(P,B) - d(P,C)}

The inequality |d(P,A) - d(P,C)| ≤ d(A,C) holds with equality
iff  P = A  or  P = C  or  P lies on line AC, but not on segment AC.

The inequality |d(P,B) - d(P,D)| ≤ d(B,D) holds with equality
iff  P = B  or  P = D  or  P lies on line BD, but not on segment BD.

Hence |f(x,y)| attains its maximum value when (x,y) is the point of intersection of
(line AC \ segment AC) and (line BD \ segment BD). (See image1.)

Taking {d(P,A) - d(P,D)} + {d(P,B) - d(P,C)} will just get an upper bound of |f(x,y)|,
not the maximum value of |f(x,y)|. (See image2.)

Hi benice;

What does d(P,A) do? Can you post it?

The distance between P and A.

Last edited by benice (2011-11-06 11:20:29)

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: max. value

Thanks benis (trying to understanding that)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: max. value

Hi benice;

It looks like you used "feasible points" to do that, I am not sure. What is your method called because it is better than mine!

---

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.