Since the function is not defined for some open interval around either c or d, a local maximum or local minimum cannot occur at this point.
An absolute maximum or minimum can occur, however, because the definition requires that the point simply be in the domain of the function.
Another application of the derivative is in finding how fast something changes.
For example, suppose you have a spherical snowball with a 70cm radius and it is melting such that the radius shrinks at a constant rate of 2 cm per minute. These types of problems are called related rates problems because you know a rate and want to find another rate that is related to it.
This type of problem is known as a "related rate" problem.
In this sort of problem, we know the rate of change of one variable (in this case, the radius) and need to find the rate of change of another variable (in this case, the volume), at a certain point in time (in this case, when ).
The reason why such a problem can be solved is that the variables themselves have a certain relation between them that can be used to find the relation between the known rate of change and the unknown rate of change.
Related rate problems can be solved through the following steps: Step one: Separate "general" and "particular" information.
The poorest performance was on steps linked to conceptual understanding, specifically steps involving the translation of prose to geometric and symbolic representations.
Overall performance was most strongly related to performance on the procedural steps.