1 / 15

Assignment 4

Assignment 4. Section 3.1 The Derivative and Tangent Line Problem. The Basic Question is…. How do you find the equation of a line that is tangent to a function y=f(x) at an arbitrary point P? To find the equation of a line you need: a point and a slope.

artie
Download Presentation

Assignment 4

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. Assignment 4 Section 3.1 The Derivative and Tangent Line Problem

  2. The Basic Question is… • How do you find the equation of a line that is tangent to a function y=f(x) at an arbitrary point P? • To find the equation of a line you need: a point and a slope

  3. How do you find the slope when the line is a tangent line?

  4. First, we approximate with the secant line.

  5. How do we make the approximation better? • Choose h smaller… • And smaller… • And smaller… • And smaller… • How close to zero can it get? • Infinitely

  6. Definition of slope of the tangent line If f(x) is defined on an open interval (a,b) then the slope of the tangent line to the graph of y=f(x) at an arbitrary point (x,f(x)) is given by:

  7. Example: • #6—Find the slope of the tangent line to the graph of the function at the given point. • (-2, -2)

  8. The limit that is the slope of the tangent line is actually much more.. • Definition of the Derivative of a Function The derivative of f at x is given by Provided the limit exists. For all x for which the limit exists, is a function of x.

  9. Notations for derivative

  10. Find the derivative by the limit process. #20 #24

  11. Find an equation of the tangent line to th graph of f at the given point. • #26 • ( - 3, 4)

  12. #34 Find an equation of the line that is tangent to the graph of f and parallel to the given line.

  13. Sketch the graph of f’ #46

  14. What destroys the derivative at a point? • Cusps • Corners • Vertical tangents

  15. And…Points of Discontinuity Fact: If a function is differentiable at x=c, then f is continuous at x=c

More Related