Second derivative test

The  exercise appears under the Differential calculus Math Mission. This exercise practices the second derivative test as a justification for the type of extreme value in a graph.

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


 * 1) Use the second derivative to determine the extreme value: This problem provides a function and possibly a critical point. The student is expected to find the value of the second derivative at the point and use it to determine if the value is a relative maximum or a minimum.Sdt1.png

Strategies
Knowledge of extrema and the picture of the graph, in particular the second derivative test, are encouraged to ensure success on this exercise.
 * 1) A critical point is where the derivative is either equal to zero or undefined.
 * 2) When a critical point is on a concave up interval, it is a relative minimum.
 * 3) When a critical point occurs on a concave down interval, it is a relative maximum.

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.