An extreme point of a function is calculated in this way:
- first, differentiate the expression of the function;
- after that, solve the equation of the differentiated function.
In the point where the first derivative is cancelling, the function has a minimum or maximum point.
We know that maximum or minimum points could be either relative, or absolute. The relative maximum or minimum is also called the local maximum or minimum. That means that the tangent to the graph of function in the point where the first derivative is cancelling, is horizontal but is not the highest or lowest value of the function.
An absolute maximum or minimum is the point where the tangent is horizontal and there is no other value of the function higer or lower than this one.
Note that the relative maximum or minimum could be an absolute maximum or minimum.