Recognizing concavity

The  exercise appears under the Differential calculus Math Mission. This exercise practices recognizing when a graph is concave up or down and how it related to increasing and decreasing.

Types of Problems
There is one type of problem in this exercise:


 * 1) Move the slider to the correct position: This problem provides a graph and a slider that is on the graph. The student is asked to move the slider to the position that represents the correct place where the function has the correct derivative and second derivative.Reccon1.png

Strategies
Knowledge of extrema and interpretation of graphs, particular concavity, are encouraged to ensure success on this exercise.
 * 1) When f'>0, a function is increasing and when f'<0 a function is decreasing.
 * 2) When f>0, a function is concave up or "smiley" and when f<0 a function is concave down or frowny.

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.