What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9

It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.

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Instructional Ideas

  • Use the video to introduce average value of a function
Classroom Considerations

  • Scholars should be familiar with the slope formula
  • Builds on prior knowledge from the series
  • Ninth installment of an 11-part YouTube playlist
Pros

  • Shows how topic can be useful in real-world contexts
  • Thorough explanations and descriptions make the concept clear
Cons

  • None