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Math Help - Multi-variable calculus - Stationary points.

  1. #1
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    Multi-variable calculus - Stationary points.

    I need to find and classify stationary points of:

    z = x^2 + 4xy + 4y - 9x + 1

    so far I got:

    dz/dx = 2x + 4y - 9 and dz/dy = 4x + 4

    not sure as to how to go on as Im rubbish at these lol

    Thanks
    Last edited by mr fantastic; July 8th 2011 at 02:10 PM. Reason: Title.
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  2. #2
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    Re: Stationary points.. HELP!!

    Quote Originally Posted by zana View Post
    I need to find and classify stationary points of:

    z = x^2 + 4xy + 4y - 9x + 1

    so far I got:

    dz/dx = 2x + 4y - 9 and dz/dy = 4x + 4

    not sure as to how to go on as Im rubbish at these lol

    Thanks
    First you need to solve the system:

    dz/dx=0
    dz/dy=0

    which will give the stationary point/s that you will then need to classify

    CB
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    Re: Multi-variable calculus - Stationary points.

    i know i need to obtain 2 simultaneous equations and substitute x but thats what im stuck on, all i get is x = y which im sure isnt right
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    Re: Multi-variable calculus - Stationary points.

    Quote Originally Posted by zana View Post
    i know i need to obtain 2 simultaneous equations and substitute x but thats what im stuck on, all i get is x = y which im sure isnt right
    Your two equations are (we have already told you what they are using your partial derivatives of z):

    dz/dx = 2x + 4y - 9=0

    and:

    dz/dy = 4x + 4=0.

    The second of these tells you that for any critical point x=-1, so using the first you find 4y-11=0 or y=11/4.

    So now you have the critical point, now you need to determine what type it is.

    CB
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    Re: Multi-variable calculus - Stationary points.

    thank you so much!
    calculus is the one bit that gets me.
    this is going to sound like a silly question but could you possibly show me how you get x=-1??
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  6. #6
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    Re: Multi-variable calculus - Stationary points.

    Surely you can solve 4x + 4 = 0...
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  7. #7
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    Re: Multi-variable calculus - Stationary points.

    Quote Originally Posted by zana View Post
    thank you so much!
    calculus is the one bit that gets me.
    this is going to sound like a silly question but could you possibly show me how you get x=-1??
    I told you that you use the second equation, which was 4x+4=0. Solving this is elementary common algebra and if you are having difficulties with it then you should reconsider your pursuit of calculus before you have reviewed/achieved fluency in algebra.

    CB
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