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Two Variable 2nd Order Taylor Series Approximation

  1. Oct 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Derive the Derive the two variable second order Taylor series approximation,
    below, to [itex]f(x,y) = x^3 + y^3 – 7xy[/itex] centred at [itex](a,b) = (6,‐4)[/itex]

    [itex]f(x,y) ≈ Q(x,y) = f(a,b) + \frac{∂f}{∂x}| (x-a) + \frac{∂f}{∂x}|(y-b) + \frac{1}{2!}[\frac{∂^2f}{∂x^2}| (x-a)^2 + 2\frac{∂^2f}{∂x∂y}\ |(x-a)(y-b)+ \frac{∂^2f}{dy^2}\ |(y-b)^2][/itex]



    2. Relevant equations



    3. The attempt at a solution
    I do not understand the question. Please help me start out. Thanks
     
    Last edited: Oct 19, 2012
  2. jcsd
  3. Oct 19, 2012 #2
    Evaluating the Taylor expansion is pretty straightforward. All you need to do is to calculate the partial derivatives, and then evaluate them at the given point. So calculate [itex] \frac{\partial f(x,y)}{\partial x} [/itex]*and then evaluate it at (x=6,y=-4). Then do the same for all other derivatives and plug the numbers you get into the expression.
     
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