Statement :  If changes from positive to negative at then has a relative maximum at .

From the increasing and decreasing function :

1. If for all in , then is decreasing on .

2. If for all in , then is increasing on .

Using the above conditions we can notice that the function is increasing on the left and decreasing on the right side of as changes from positive to negative at .

The function has a maximum at since it changes its sign.

If changes from positive to negative at then has a relative maximum at .