Increasing and decreasing functions
You can determine whether a function is increasing or decreasing on a given interval by using the derivative of the function.
Consider the following two facts:
Example 1:
Note: When we are reffering to intervals we mean the the range of numbers x lies in which the function is increasing or decreasing.
For example:
The graph is increasing on the interval [-2,0] so this refers to real values satisfying -2< x < 0. The graph is also decreasing on the interval [0,2] so this refers to real values satisfying 0 < x < 2.
It is also possible to have functions in which they are increasing or decreasing for all real values of x. Questions have come up in which you would need to prove that a certain function is increasing or decreasing for all values of x.
Example 2:
Practice Question:
