Answer:
To express the function f(xy) = x^2 + 3y^2 - 9x - 9y + 26 as Taylor’s Series expansion about the point (1, 2), we need to find the partial derivatives of f with respect to x and y, and evaluate them at (1, 2). Then, we can use these values to form the Taylor’s Series expansion.
∂f/∂x = 2x - 9
∂f/∂y = 6y - 9
Evaluating these partial derivatives at (1, 2) gives:
∂f/∂x(1, 2) = 2(1) - 9 = -7
∂f/∂y(1, 2) = 6(2) - 9 = 3
Now, we can form the Taylor’s Series expansion:
f(x,y) = f(1,2) + (-7)(x-1) + (3)(y-2) + higher-order terms
where the higher-order terms involve second-order partial derivatives of f and higher powers of (x-1) and (y-2).