Chapter 5 CA5: Linear Approximations
In Math1110 we looked at the idea of “the linearization of a function of one variable”. The idea was that near the point \(x=x_0\) we could approximate the function \(f(x)\) using the line tangent to the function at \(x=x_0\text{.}\) We called this tangent the linearization of the function at \(x=x_0\) and used it to derive the “linear approximation formula”,
\begin{equation*}
\Delta y \simeq f'(x_0) \Delta x\text{.}
\end{equation*}
These ideas can also be applied to functions of two variables.