Education Technology

Calculus: First Derivative Test

by Texas Instruments


  • Relate the first derivative of a function to its critical points and identify which of these critical points are local extrema.
  • Visualize why the first derivative test works and how it is used to determine local minima and maxima.


  • first derivative
  • critical point
  • local maximum, local minimum, extrema

About the Lesson

This lesson involves visualizing the connections between the first derivative of a function, critical points, and local extrema. As a result, students will:

  • Develop an understanding of the first derivative test.
  • Explore a sequence of functions, some by moving a tangent line along the function graph and noting changes in the first derivative of a function near its critical points.
  • Build on their familiarity with the concept of the derivative at a point as the local slope of the function graph at that point.