Local Linear Approximation vs Linearization

[Lebombo]

Are Local Linear Approximation, Linear Approximation, and Linearization all the same thing?


Question is, I learned about something called Local Linear Approximation in Calc 1. Now in Calc 2, the topic of Linearization from Calc 1 was mentioned. But I never did anything that was referred to as Linearization. The closest sounding topic was Local Linear Approximation. So are they the same exact topic just referred to with different names?

 

[HallsofIvy]

Perhaps a slight difference. When you have a "local linear approximation", what is "local" is already decided. That is, you have a specific point at which you approximate the curve by a line. The "linearization" of a function requires a choice of the point at which you will linearize. "Linearization" of the same function at two different "x" values will give two different linear functions.

Once you have chosen that point at which to linearize the function, then linearization about that point is the local linear approximation.