Given a function, you have the right to easily uncover the slope of a tangent line utilizing Microsoft Excel to carry out the dirty work. The is to say, you deserve to input your x-value, develop a couple of formulas, and also have Excel calculation the secant worth of the tangent slope. This is a fantastic tool for Stewart Calculus sections 2.1 and 2.2.

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Note the you can essentially enter the specific same attributes into Google Sheets as well as Excel, therefore this is a good tool because that either option. For this reason if you have actually a windows or Mac an equipment with Excel installed, usage that. If you"re to run a Linux distro or Chrome OS, or would fairly use a cost-free tool, use Google Sheets.

Getting Started

For this example, we"ll use the following function:

f(x)=2+SQRT(x); x=1

To translate, we want the to find the steep of the tangent heat of the duty 2+SQRT(x) where x=1.

Image via Robert Talbert

Step 1: find the Y-Coordinate

Using the formula, it"s quite straightforward to discover the y-coordinate based upon the x-value. Because that example, because that x=1, the y-coordinate would be F(1)=2+SQRT(1), bring about a worth of 3.

Image via Robert Talbert

Step 2: Secant Lines

Now we"ll have to use point out both before and after the x-value that technique that value, however never reach it (purple line below). Plotting these points on the graph will develop the secant line because that the formula.

Image via Robert Talbert

Now it"s time to begin plotting. We"ll begin with hand calculations before moving ~ above to using Excel (or Sheets) to automate the process.

We"ll should plot points for the x-value, the y-value, and also the secant slope.

Image via Robert Talbert

As you deserve to see above, with x=2, the y-value is 3.4142 (using the formula). The secant slope is calculate by taking the distinction in the y-value and dividing the by the distinction in the x-value, i beg your pardon is 0.4142.

Step 3: Automate Y-Value v Excel

Recall the we desire the x-value to approach 1 without ever reaching it. So, we deserve to use 2, 1.5, 1.1, 1.01, and 1.001. You"ll also want to execute this comes the other way, so we have the right to use 0, 0.5, 0.9, 0.99, and 0.999.

Start through labeling the columns, then get in your x-values. We"ll begin with 2 together it ideologies 1.

Now enter the formula to calculate the y-value. In the 2nd column, intake "=2 + sqrt(A2)" wherein A2 is the box where the x-value is save (you can enter "A2" manually, or merely click the box that contains the value), climate hit enter.

Now click the box that girlfriend just entered the formula into, then traction from the bottom-right of the box under to the last x-value to insert the formula right into each one—you"ll notice the y-values popular music up.

Step 4: Automate Secant Slope with Excel

Now in the third column, let"s enter the formula to calculate the secant slope. The formula below is "=(B2 - 3)/(A2 - 1)" (again, you can simply click on the box that hold the value).

Just as before, drag down from the bottom-right to use the formula because that the rest of the x- and y-values.

Step 5: calculation for X-Values native 0 draw close 1

Now simply rinse-and-repeat, using x-values walk the various other way. Apply the very same drag an approach for these.

There you have it, the secant slopes for this formula when x=1. For a more detail, check out the video clip below.

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