3.9 Linear Approximations and Differentials

OpenStax Calculus Volume 1 — Section 3.9

Learning Objectives

  • Find the linearization \(L(x) = f(a) + f'(a)(x - a)\) of a function at a point

  • Use linearization to approximate function values near \(a\)

  • Define differentials \(dy = f'(x) \, dx\) and interpret geometrically

  • Estimate error and relative error using differentials

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.