Let's say I've got a graph describing Coolmath's revenue...

a graph of increasing, then decreasing, then increasing revenue

Let's plop some tangent lines in there:

a graph of revenue with tangent lines...  they show the slopes of the graph at the points where they're located

It's pretty clear that the tangent lines with positive slopes are good (yea - profits are going up)... and tangent lines with negative slopes are bad (boo - profits are going down.)

So, slopes of tangent lines can tell us where a graph is increasing or decreasing.

But, we can use tangent lines to tell us even more than that.