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Lagrange multiplier method

  1. Mar 9, 2007 #1
    Question:

    Use Lagrange multiplier method to determine the point on the curve
    y=1-[tex]x^2[/tex]
    that maximises the function f(x,y)=2x + y.
    Hence find the maximum value of f.

    Attempt at Solution:

    Okay I used the Lagrange method to get a point on the curve and I got (1,0)

    How do I find the maximum value of f though?
     
  2. jcsd
  3. Mar 9, 2007 #2

    cristo

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    If you've found the values of x and y where the function has a maximum, then do you not just plug (1,0) into f(x,y) to obtain the value of the function at that point?
     
  4. Mar 9, 2007 #3

    Dick

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    Uh, substitute (1,0) into f?
     
  5. Mar 9, 2007 #4
    i get (0,0)?
     
  6. Mar 9, 2007 #5

    Dick

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    f is a number. Not a point. And it's not 0.
     
  7. Mar 9, 2007 #6
    i'm still stuck! i don't what to do lol
    give me more tips before i give up on maths altogether!!
    (does anyone else go through a phase when they just want to give up? lol)
     
  8. Mar 9, 2007 #7

    Dick

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    You say f(x,y)=2*x+y. You've found a solution (1,0) so x=1, y=0. What is f(x,y)? Don't get so flustered!
     
  9. Mar 9, 2007 #8
    'Don't get so flustered!'

    you don't know what kind of day i've had! lol

    thank you for your help and time i'm sure it's not a hard question i'll think about it tomorrow when i feel more awake.
     
  10. Mar 9, 2007 #9

    Dick

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    Your annoyance is blocking you from seeing the obvious. That makes it a really good time to take a rest.
     
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