The Tangent Line Problem

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

How do you find the slope of the tangent line to a function at a point Q when you only have that one point? This Demonstration shows that a secant line can be used to approximate the tangent line. The secant line PQ connects the point of tangency to another point P on the graph of the function. As the distance between the two points decreases, the secant line becomes closer to the tangent line.

Contributed by: Samuel Leung and Michael Largey (March 2011)
Open content licensed under CC BY-NC-SA



Usually, the slope of a line through two points and is calculated using the formula . This method, however, requires that you know two points; in the tangent line problem, you know only one point. In this case, the slope of the tangent line can be approximated through the use of a limit, , where is the horizontal distance between the point of tangency and another point. This Demonstration lets you manipulate the value of and shows how this affects the slope of the secant line.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.