What is the difference between a relative max. or min. and an absolute maximum or minimum value?

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.