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.

Concepts

area under a curve, integrals, averages, fundamental theorem of calculus, antiderivatives

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Additional Tags

math

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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

• This video is hosted on YouTube

Pros

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

Cons

• None