# Two Variable 2nd Order Taylor Series Approximation

1. Oct 19, 2012

### manager77

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

3. The attempt at a solution
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 $\frac{\partial f(x,y)}{\partial x}$*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.