Objectives: In this tutorial, we define what is meant by a function that is concave upward or concave downward on some interval. Two geometrical conditions and two conditions using the derivative and second derivative are used to make this definition. Some examples of finding graphically where a given function is concave upward or concave downward are given. Inflection points are also defined. There are three quizzes that test the relationships between the graph of a function and information about its derivatives. After working through these materials, the student should be able