Wksht 3: Equation of Tangent Line

Question!

What pieces of information do we need to determine the equation of a line?

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If you weren't sure about the answer to the question, take a look at this website for a refresher on Point-Slope Form.

To find the equation of the line tangent to at the point where , we need the slope of the tangent line, , and one point on the line- in this case, our point will be at .

First, let's take a look at the graph of the function.

The Point

To find the point we will be using, we find . This is done algebraically in the Solution pdf at the end of the page. Graphically, we see that the point is .

The Slope

To find the slope of the tangent line, we will use . This is done algebraically in the Solution pdf at the end of the page. We will use a graph to determine the slope of the tangent line:

Use the slider to see what happens to m when the value of h gets very small.

From the graph above, we can see that as h nears 0, m nears 24. Therefore,

Building the Equation

To create the equation of the line whose slope is 24, and contains the point , we use point-slope form, plugging into: .

Question 2!

What is the equation of the line tangent to f at x=2?

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