When we consider the graph of a function certain points and features are particularly noteworthy.
In the display on the right some of the noteworthy features are:
1. Where the graph cuts the x-axis. See points A, B and C on the right.
2. Where the graph cut the y-axis. See point D on the right.
3. Any turning points the graph has. See points E and F on the right.
At these points the gradient is zero. E is a local maximum. there may be points on the graph that are higher than E but in the locality of point E it is the highest point.
Looking at the section of the graph displayed the highest point overall is at the right hand end. This would be the global maximum for the section displayed.
From the extreme left of the display up to points E the gradient is positive.
We say that the function is increasing over this interval. The function is decreasing from E to F and then increases again from F onwards.