Two Variable 2nd Order Taylor Series Approximation

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Homework Statement



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]



Homework Equations





The Attempt at a Solution


I do not understand the question. Please help me start out. Thanks
 
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Answers and Replies

  • #2
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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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