Linear approximation, or linearization, is a method we can use to approximate the value of a function at a particular point. The reason liner approximation is useful is because it can be difficult to find the value of a function at a particular point.

What is the difference between linearization and differentials?

For a brief but sloppy explanation of the difference: The differential consists of just the slope. The linear approximation consists of both the value and the slope.

What are the advantages to Linearizing data that is nonlinear to start with?

This process is called a linearization of the data. This does not change the fundamental relationship or what it represents, but it does change how the graph looks. The advantage of linearizing non-linear data is that the analysis of the parameters (slope and intercept) becomes significantly easier.