# Write an equation of the line tangent to the graph of f

We will start with the same curve and the same point, but add a second point on the curve some distance away from the original point.

At each point, the moving line is always tangent to the curve. Also, do not worry about how I got the exact or approximate slopes.

## Find the slope of the tangent line to the graph of the function at the given point

At most points, the tangent touches the curve without crossing it though it may, when continued, cross the curve at other places away from the point of tangent. This is all that we know about the tangent line. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Looking at these problems here will allow us to start to understand just what a limit is and what it can tell us about a function. In fact, this is how a tangent line will be defined. Conversely, it may happen that the curve lies entirely on one side of a straight line passing through a point on it, and yet this straight line is not a tangent line. Due to the nature of the mathematics on this site it is best views in landscape mode. So here is how we can "approach" that tangent line as a limit. In general, we will think of a line and a graph as being parallel at a point if they are both moving in the same direction at that point.

However, we would like an estimate that is at least somewhat close the actual value. If you are viewing this on the web, the image below shows this process.

Looking at these problems here will allow us to start to understand just what a limit is and what it can tell us about a function. There are two reasons for looking at these problems now.

So, looking at it now will get us to start thinking about it from the very beginning.

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