How To Draw A Tangent Line In Excel

Given a function, you lot can easily find the slope of a tangent line using Microsoft Excel to do the muddy work. That is to say, you can input your x-value, create a couple of formulas, and have Excel calculate the secant value of the tangent gradient. This is a fantastic tool for Stewart Calculus sections ii.1 and ii.2.

Note that you lot can essentially enter the exact same functions into Google Sheets as well every bit Excel, so this is a great tool for either option. So if you lot have a Windows or Mac motorcar with Excel installed, apply that. If you're running a Linux distro or Chrome OS, or would rather use a complimentary tool, utilise Google Sheets.

Getting Started

For this example, we'll use the post-obit part:

To translate, nosotros desire the to find the slope of the tangent line of the function two+SQRT(x) where x=one.

Image via Robert Talbert

Step 1: Find the Y-Coordinate

Using the formula, it's quite unproblematic to discover the y-coordinate based on the x-value. For example, for x=1, the y-coordinate would exist F(one)=2+SQRT(1), leading to a value of 3.

Image via Robert Talbert

Step ii: Secant Lines

Now nosotros'll need to use points both earlier and subsequently the x-value that approach that value, but never achieve it (purple line below). Plotting these points on the graph will create the secant line for the formula.

Image via Robert Talbert

Now information technology's time to start plotting. We'll starting time with hand calculations earlier moving on to using Excel (or Sheets) to automate the procedure.

We'll demand to plot points for the x-value, the y-value, and the secant slope.

Epitome via Robert Talbert

Every bit you tin encounter above, with ten=2, the y-value is 3.4142 (using the formula). The secant slope is calculated by taking the difference in the y-value and dividing information technology past the difference in the x-value, which is 0.4142.

Step iii: Automate Y-Value with Excel

Call up that we want the ten-value to approach 1 without ever reaching it. So, we can use 2, i.5, 1.1, ane.01, and 1.001. You'll also want to do this coming the other way, so nosotros tin utilise 0, 0.5, 0.9, 0.99, and 0.999.

Start past labeling the columns, and so enter your x-values. We'll start with 2 as it approaches one.

Now enter the formula to calculate the y-value. In the second column, input "=two + sqrt(A2)" where A2 is the box where the x-value is stored (yous tin can enter "A2" manually, or simply click the box that contains the value), then hit enter.

Now click on the box that you just entered the formula into, and then drag from the bottom-right of that box down to the final x-value to insert the formula into each one—you'll discover the y-values popular upwardly.

Step 4: Automate Secant Slope with Excel

Now in the third column, let'south enter the formula to summate the secant slope. The formula here is "=(B2 - 3)/(A2 - 1)" (again, yous can simply click on the boxes that hold the value).

But as earlier, drag downward from the bottom-right to apply the formula for the rest of the x- and y-values.

Step 5: Calculate for X-Values from 0 Approaching 1

Now merely rinse-and-repeat, using 10-values going the other way. Apply the same drag technique for these.

There you have information technology, the secant slopes for this formula when x=i. For a further detail, check out the video below.

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Screenshots via WonderHowTo unless otherwise noted

Source: https://ms-office.wonderhowto.com/how-to/create-tangent-line-with-excel-424513/

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