Final answer:
The equation for the tangent plane to z=f(x,y) at (3,-2) can be found using the gradient vector.
Step-by-step explanation:
The equation for the tangent plane to z=f(x,y) at (3,-2) can be found using the gradient vector. The gradient vector is the vector formed by the partial derivatives of f(x,y) with respect to x and y. So, let's say the partial derivative of f(x,y) with respect to x is g(x,y) and the partial derivative of f(x,y) with respect to y is h(x,y), then the equation of the tangent plane is:
z = f(3,-2) + g(3,-2)(x - 3) + h(3,-2)(y + 2)