Increasing or Decreasing Derviative from Function

In this lesson, students are taught to determine when the rate of change of a function is increasing or decreasing by looking at the Cartesian graph of the derivative of the function. The lesson also discusses the concept of inflection points, which are essential for determining when the derivative ceases to decrease and starts to increase, or vice versa. Students are shown examples of functions such as the logistic function and how inflection points help to separate the derivative from increasing or decreasing.

Given a Cartesian graph of the derivative of a function be able to determine when the function is increasing
and decreasing or has obtained an extrema.

• How can you tell whether the derivative of a function is increasing or decreasing given a function?
• Where is the maximum or minimum of the graph of the derivative of a function?
• What does the inflection point of a graph tell you about the graph of the derivative of the function?