Concavity and the second derivative | |
---|---|
Description | |
Exercise Name: | Concavity and the second derivative |
Math Missions: | Differential calculus Math Mission |
Types of Problems: | 2 |
The Concavity and the second derivative 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:
- Fill in the chart: This problem has a graph and a chart with several claims about the function in the graph. The user is expected to use the drop down menus in the chart to complete the chart correctly.
- Use the graph to answer the concavity question: This problem has a graph and some question about the graph. The user is expected to use the graph and answer with the appropriate interval from the list below.
Strategies[]
Knowledge of derivatives and the meaning of concavity are encouraged to ensure success on this exercise.
- A function is increasing if the derivative is positive, and decreasing when it is negative.
- A function is concave up if the second derivative is positive, and concave down when it is negative.
- A function looks "smiley" when it is concave up and "frowny" when it is concave down.
- A critical point is when the derivative is zero, and an inflection point is when a function changes concavity.
Real-life Applications[]
- Most of the problems in this subsection are applications in some sense, so the majority of the exercises are applications also.
- Calculus has massive applications to physics, chemistry, biology, economics and many other fields.