Report an Error. Explanation : One way of finding the slope at a given point is by finding the derivative. Using the exponential rule we get the following derivative,. Note that in this case, using the y coordinate was not necessary. The first derivative is and for this function and So the slope is. The first derivative is and for this function and plugging in the specific x value we get, So the slope is. Copyright Notice.

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## what is the slope of the tangent line of the graph of f(x)

Report an issue with this question If you've found an issue with this question, please let us know. Do not fill in this field. Louis, MO Or fill out the form below:. Company name. Copyright holder you represent if other than yourself. We know from algebra that to find the equation of a line we need either two points on the line or a single point on the line and the slope of the line. Since we know that we are after a tangent line we do have a point that is on the line.

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Now we reach the problem. This is all that we know about the tangent line. In order to find the tangent line we need either a second point or the slope of the tangent line. We can see from this graph that the secant and tangent lines are somewhat similar and so the slope of the secant line should be somewhat close to the actual slope of the tangent line. 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. Also, do not worry about how I got the exact or approximate slopes.

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Therefore, we should always take a look at what is happening on both sides of the point in question when doing this kind of process. As noted above, this is the correct value and we will be able to prove this eventually.

There are a couple of important points to note about our work above. In this kind of process it is important to never assume that what is happening on one side of a point will also be happening on the other side as well.

## Calculus I - Tangent Lines and Rates of Change

We should always look at what is happening on both sides of the point. In this example we could sketch a graph and from that guess that what is happening on one side will also be happening on the other, but we will usually not have the graphs in front of us or be able to easily get them.

The next thing to notice is really a warning more than anything. In most cases this will not be the case. You should always use at least four points, on each side to get the estimate.

## The easiest way to calculate the tangent of a function

Two points is never sufficient to get a good estimate and three points will also often not be sufficient to get a good estimate. This option controls the return value of the function. This is the default. By default, this point is plotted as a blue circle. By default, the value is true. Whether the tangent line is plotted. A list of options for the plot of the tangent line.

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By default, this is plotted as a solid blue line. A caption for the plot. The default caption is constructed from the parameters and the command options. See Also.