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  • MA101: Single-Variable Calculus I
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  • Course Introduction
  • Unit 1: Analytic Geometry
  • Unit 2: Instantaneous Rate of Change: The Derivative
  • Unit 3: Rules for Finding Derivatives
  • Unit 4: Transcendental Functions
  • Unit 5: Curve Sketching
  • Unit 6: Applications of the Derivative
  • Unit 7: Integration
  • Unit 8: Applications of Integration
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MA101: Single-Variable Calculus I

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  6. Unit 2: Instantaneous Rate of Change: The Derivative
  7. 2.1: The Slope of a Function
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  • 2.1: The Slope of a Function

    • In this subunit, you will look at the first of two major problems that lie at the heart of calculus: the tangent line problem. This intellectual exercise demonstrates the origins of derivatives for nonlinear functions.

    • Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.1: The Slope of a Function" URL

      Read Section 2.1 (pages 29-33). You will be introduced to the notion of a derivative through studying a specific example. The example will also reveal the necessity of having a precise definition for the limit of a function.

    • Massachusetts Institute of Technology: David Jerison's "Rate of Change" Page

      Watch this video. In this lecture, Jerison introduces the notion of a derivative as the rate of change of a function, or the slope of the tangent line to a function at a point.

    • Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Exercises 2.1, Problems 1 - 6" URL

      Work through problems 1-6 for Exercise 2.1. When you are done, check your answers against Appendix A.

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