Visualize the connections between the first derivative of a function, critical points, and local extrema.
- 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.