Final answer:
To find the tangent plane to the equation at the point (4, 2, 12), we need to determine the partial derivatives of the equation with respect to each variable and evaluate them at the given point. The equation of the tangent plane is obtained by substituting the values into the equation.
Step-by-step explanation:
To find the tangent plane to the equation at the point (4, 2, 12), we need to determine the partial derivatives of the equation with respect to each variable. Let's assume the equation is f(x, y, z). The partial derivatives are denoted as ∂f/∂x, ∂f/∂y, and ∂f/∂z. Then, we evaluate these partial derivatives at the point (4, 2, 12). The equation of the tangent plane is given by the equation:
(x - 4) * (∂f/∂x) + (y - 2) * (∂f/∂y) + (z - 12) * (∂f/∂z) = 0