1. Increasing and Decreasing Functions
   For a function and any two numbers and in a given interval:
1. If and , the function is said to be increasing on that interval.
2. If and , the function is said to be decreasing on that interval.


2. Criteria for Increasing and Decreasing Functions
   If a function is differentiable on an interval and for all in that interval:
1. If , the function is increasing on that interval.
2. If , the function is decreasing on that interval.




3. : The Converse is Not Always True
   In general, the converse of the above is not true. for example, the function is increasing on the interval because, for any ,
   
   which implies . However, the derivative equals zero at . Therefore, the function is increasing even though .