Lesson Plan: Equations of Tangent Lines and Normal Lines Mathematics • Higher Education

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the slope and equation of the tangent and normal to a curve at a given point using derivatives.


Students will be able to

  • find the equation of the tangent to a curve at a given point,
  • find the equation of the normal to a curve at a given point,
  • find the point on the curve at which the normal or tangent is parallel or perpendicular to a given line,
  • find the point at which two curves meet orthogonally.


Students should already be familiar with

  • differentiating polynomial, trigonometric, rational, and radical functions,
  • completing an equation given the slope of the tangent to the curve at a given point,
  • the chain, product, and quotient rules of differentiation.


Students will not cover

  • implicitly defined curves,
  • differentiation of reciprocal trigonometric functions.

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