Lesson Plan: Average and Instantaneous Rates of Change Mathematics • Higher Education

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the average rate of change of a function between two 𝑥-values and use limits to find the instantaneous rate of change.

Objectives

Students will be able to

  • evaluate the average rate of change of a given function over an interval,
  • find an expression of the average rate of change of a given function over a general interval, 𝑥 to 𝑥+,
  • use limits to find the instantaneous rate of change of a function at a point,
  • use limits to find an expression of the instantaneous rate of change of a given function at a general point, 𝑥,
  • find the average rate of change and instantaneous rate of change in the context of a real world system.

Prerequisites

Students should already be familiar with

  • limits and limit notation,
  • graphs of polynomial functions,
  • tangent lines,
  • secant lines.

Exclusions

Students will not cover

  • considering the rate of change as a function,
  • the definition of the derivative,
  • differentiation.

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