Increasing and Decreasing Intervals and Extrema
- In calculus (and in life), much effort is devoted to determining the behavior of something. In calculus's case, the effort is put into determining the behavior of a function on an interval. Various questions about the behavior of functions on an interval include:
- Does have a maximum value on said interval?
- Does it have a minimum value?
- Where is the function increasing?
- Where is it decreasing?
- Answers to these types of questions have tremendous implications to real world applications.
- In this section, you will learn how derivatives can be used to relative extrema as either relative minima or relative maxima. First, it is important to define increasing and decreasing functions.
- A function is increasing if, its graph moves up, and is decreasing if its graph moves down. A positive derivative implies that the function is increasing; a negative derivative implies that the function is decreasing; and a zero derivative on an entire interval implies that the function is constant on that interval.