Tangent Plane

Suppose \(f\) has continuous partial derivatives. An equation of the tangent plane to the surface \(z = f(x, y)\) at the point \(P(x_0, y_0, z_0)\) is

\[ z - z_0 = f_x(x_0, y_0)(x - x_0) + f_y(x_0, y_0)(y - y_0) \]

EXAMPLE 1
Find the tangent plane to the elliptic paraboloid \(z = 2x^2 + y^2\) at the point \((1, 1, 3)\).