If a function z = g(x, y) has g(1, 2) = 10, gx(1, 2) = 7 and gy(1, 2) = -5, find the equation of the plane tangent to the surface z = g(x, y) at the point where x = 1 and y = 2.
I understand how to do the question when an equation is given but without it, I am lost. Could someone help me get started through the problem.
Since the equation for the surface is , you can do a linear estimate:
which is the equation of the tangent plane. Of course is just -1 in this case.