Unit 3

Curve Sketching

Lesson 2: Increasing and Decreasing Functions


There are several relationships between a function and its derivative. In this lesson you will explore one relationship in detail.

Interactive


Click the interactive button to open the applet Where is the Derivative Positive? The applet shows a polynomial function that can be transformed by moving the points on the graph.

  • Predict the regions where the derivative of this function will be positive and where it will be negative.
  • Use the checkboxes to check your prediction.
  • Move some points on the graph of the original function and try again.
What characteristic(s) on the graph of the original function allow you to determine whether the derivative of that function will be positive or negative?