Final answer:
The linearization L(x,y) of f(x,y) at the point (3,2) requires finding the tangent plane to the surface at that point, using the function's value and its partial derivatives at that point.
Step-by-step explanation:
The linearization L(x,y) of a function f(x,y) at a point (3,2) is the process of finding the best linear approximation to f near that point, which involves finding the equation of the tangent plane to the surface at that point. This approximation is given by the equation:
L(x,y) = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)
where fx and fy are the partial derivatives of f with respect to x and y, and (a,b) is the point at which the linearization is computed. In your case, the function f is not provided, but the process would involve calculating these derivatives and evaluating them at the point (3,2).