Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in February 2022. The graphs are generated using Desmos. This work is licensed under a Creative Commons BY 4.0 International License.
Derivatives, by definition, are the slope of the tangent line on a specific point on a curve.
To create the equation of the tangent line, use the point slope form of a linear equation and replace the point and the slope with the appropriate information from the curve.
The slope of the tangent will be the value of the derivative at the tangential point, while the point itself will be populated by the x value and the value of the original function in the y-point.
Here is an example of how this looks visually:
