Linearization of Multivariable Functions
In single variable functions, it was possible to draw a tangent line that touches the function at a certain point $a$. Similarly, in Multivariable Functions, it is possible to draw a tangent plane to the surface of the function, which linearizes that function at the point $(a,b)$ and at points close to it. The linearized plane’s function at $(a,b)$ is calculated by:
$$ L(x) = f(a,b) + \frac{\partial f}{\partial x}(x-a) + \frac{\partial f}{\partial y}(y-b) $$