Concavity and the second derivative

The  exercise appears under the Differential calculus Math Mission. This exercise explores the relationship between concavity and a graph.

Types of Problems
There are two types of problems in this exercise:


 * 1) Fill in the chart: This problem has a graph and a chart with several claims about the function in the graph. The student is expected to use the drop down menus in the chart to complete the chart correctly.Catsd1.png
 * 2) Use the graph to answer the concavity question: This problem has a graph and some question about the graph. The student is expected to use the graph and answer with the appropriate interval from the list below.Catsd2.png

Strategies
Knowledge of derivatives and the meaning of concavity are encouraged to ensure success on this exercise.
 * 1) A function is increasing if the derivative is positive, and decreasing when it is negative.
 * 2) A function is concave up if the second derivative is positive, and concave down when it is negative.
 * 3) A function looks "smiley" when it is concave up and "frowny" when it is concave down.
 * 4) A critical point is when the derivative is zero, and an inflection point is when a function changes concavity.

Real-life Applications

 * 1) Most of the problems in this subsection are applications in some sense, so the majority of the exercises are applications also.