Lesson Plan: Curve Sketching using Derivatives Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use derivatives to graph a function.


Students will be able to

  • identify the graph of a given function by considering the derivative of the function,
  • use local extrema and intervals of increase and decrease to help sketch the graph of a function,
  • use limits to find vertical and horizontal asymptotes of the graph of a function and its end behavior,
  • use the second derivative, points of inflection, and concavity of a polynomial or rational function to help sketch the graph of a function.


Students should already be familiar with

  • using chain,product, and quotient rule to differentiate functions,
  • finding and identifying the critical points of a function using the first and second derivatives of that function,
  • finding the intervals of increase and decrease of a function,
  • finding the points of inflection of a function,
  • finding the concavity of a curve along different sections of it.


Students will not cover

  • oblique asymptotes.

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