Activity 11.6.2

Find the equation of the tangent plane to $f(x,y) = x^2y$ at the point $(1,2)$.

Suppose that the tangent plane to the graph of a continuously differentiable function $z=g(x,y)$ is given in the form $$\begin{gathered} z = 5 - 3(x+2) + (y-3) \end{gathered}$$. Use the equation of the tangent plane to identify a point on the graph as well as a value of $g_x$ and a value of $g_y$. Be sure to identify at what point(s) you have found the values of the partial derivatives.