Tangent Planes

y = f(x) has a tangent line at the point (a, f(a)) given by y - f(a) = f’(a)(x-a)

Similarly, a surface given by z = f(x, y) will have a tangent plane (a, b, f(a, b)) given by

$z-f(a,b)=\frac{\partial f}{\partial x}(a,b)(x-a)+\frac{\partial f}{\partial y}(a,b)(y-b)$