Re: number with maximum, minimum
- From: "mina_world" <mina_world@xxxxxxxxxxx>
- Date: Mon, 29 Jan 2007 14:23:26 +0900
"Jon Slaughter" <Jon_Slaughter@xxxxxxxxxxx> wrote in message
news:Exevh.36195$QU1.13452@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
"mina_world" <mina_world@xxxxxxxxxxx> wrote in message
news:epjpjj$29f$1@xxxxxxxxxxxxxxxxxxx
Hello sir~
For x, y such that {(x-1)^2} + {(y+1)^2} <= 1,
Find M/m with the maximum value M and minimum value m of (x+y+2) /
(-x+y+4).
One way is to use lagrangian multipliers.
Your function that you are trying to optimize is f(x,y) = (x+y+2) /
(-x+y+4).
and your constrant is g(x,y) = {(x-1)^2} + {(y+1)^2} = c <= 1.
Another way is to visualize your function on the disk centered at (1,-1)
and try to see if it has any "special" properties on that disk. (such as
if its maximum must be on its boundary).
What you can see is that f(x,y) is undefined at (2,-2) which is ouside
your disk but its possible that the point closest from the disk to that
point is a critical point. Ofcourse you would still have to prove this
though.
Yes, I know the Lagrange multipliers.
But...complex.
From Df = lambda*Dg,{(2y+6)/{(-x+y+4)^2} , (-2x+2)/{(-x+y+4)^2} = lamda*(2x-2, 2y+2).
How do you progress it ?
.
- References:
- number with maximum, minimum
- From: mina_world
- Re: number with maximum, minimum
- From: Jon Slaughter
- number with maximum, minimum
- Prev by Date: Re: det(A+ tB)
- Next by Date: More primality testing (was: Elementary group theory: Proof of Fermat-Maas ...)
- Previous by thread: Re: number with maximum, minimum
- Next by thread: Re: number with maximum, minimum
- Index(es):
Relevant Pages
|
