Wksht 3: Equation of Tangent Line
Exercise
Question!
What pieces of information do we need to determine the equation of a line?
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?
