3.1 Defining the Derivative

OpenStax Calculus Volume 1 — Section 3.1

Learning Objectives

  • Define the derivative using the limit: \(f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\)

  • Interpret the derivative as the slope of the tangent line

  • Interpret the derivative as an instantaneous rate of change

  • Compute derivatives from the limit definition for polynomial and simple functions

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.