Extreme values of a function

If a function is not constant a natural question is whether the function has a maximum value or a minimum value. In calculus we aren't concerned with physical barriers such as temperature going below zero kelvin or speed going beyond the speed of light. The function can have points where the maximum or minimum is local or global. It's important to say that when the limit at a point results in infinity, that point cannot be a maximum or minimum because infinity is not a number that can be reached.