Lesson Plan: Linear Approximation Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use derivatives to find the equation of the line that approximates the function near a certain value and use differentials to approximate the change in the function.


Students will be able to

  • use a tangent line to approximate a function 𝑓(𝑥) near the point of tangency,
  • understand that the equation of the tangent line approximation to 𝑓(𝑥) near a is given by 𝐿(𝑥)=𝑓(𝑎)+𝑓(𝑎)(𝑥𝑎),
  • understand whether a linear approximation is an overestimate or an underestimate when given a graph.


Students should already be familiar with

  • the chain, product, and quotient rules for differentiation,
  • differentiating polynomial, trigonometric, rational, and exponential functions.


Students will not cover

  • the mean value theorem,
  • using the second derivative to calculate whether an approximation is an overestimate or an underestimate.

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