Take a closer look at increasing and decreasing behavior by zooming in on graphs. An AP® Calculus reference document examines how increasing/decreasing behavior should be considered in terms of intervals rather than points. The resource starts off with past AP® questions that focus on determining whether a function is increasing or decreasing at a specific point, and then provides an example where looking at a specific point on a graph does not make sense.

Concepts

derivatives, velocity, trigonometric functions

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Additional Tags

math

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Instructional Ideas

• Use the resource as an extra credit activity
  

Classroom Considerations

• Pupils must be able to find derivatives of trigonometric and inverse trigonometric functions
• Scholars should have an understanding of how derivatives relate to velocity
  

Pros

• Tables and graphs are easy to read and interpret
  

Cons

• While instructors may find the information interesting, learners may not