1 / 13

The Tangent Problem

The Tangent Problem. Find an equation of the tangent line to the curve at the point (2,3). First we need to estimate the slope at the point (2,3). We are going to estimate the slope using secant lines. From the left: Using points (2,3) and (1,-1).

gunda
Download Presentation

The Tangent Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Tangent Problem Find an equation of the tangent line to the curve at the point (2,3)

  2. First we need to estimate the slope at the point (2,3).

  3. We are going to estimate the slope using secant lines

  4. From the left: Using points (2,3) and (1,-1)

  5. From the left: Using points (2,3) and (1.5, -0.375)

  6. From the left: Using points (2,3) and (1.9, 2.069)

  7. From the left: Using (2,3) and (1.99,2.9007)

  8. From the right: Using points (2,3) and (3,21)

  9. From the right: Using points (2,3) and (2.5,9.875)

  10. From the right: Using points (2,3) and (2.1, 4.071)

  11. From the right: Using (2,3) and (2.01, 3.1007)

  12. Summary of Results From both the left and the right sides, the slopes of the secant lines are approaching 10, so we can estimate that the slope of the tangent line to the point (2,3) is 10.

  13. Original Question: Find an equation of the tangent line to the curve at the point (2,3) • We know that m = 10 and we have a point (2,3), so

More Related