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 .