1 / 16

Warm Up

Warm Up. Find the slope of the tangent line to at x=2. Answer: m= -4. Derivative of a Function. 3.1. Goal. I will be able understand the relationship between a function and its derivative as well as recognize when a function will not be differentiable. New calendar . Definition.

bluma
Download Presentation

Warm Up

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. Warm Up • Find the slope of the tangent line to at x=2. • Answer: m= -4

  2. Derivative of a Function 3.1

  3. Goal • I will be able understand the relationship between a function and its derivative as well as recognize when a function will not be differentiable. • New calendar

  4. Definition • The derivative is the formula for slope of a tangent line, instantaneous speed, or velocity of an object.

  5. Formula

  6. Alternate Formula • If asked to find the derivative at a point x=a.

  7. Notation • There are many ways to denote the derivative. They can all be found at the top of page 101. • I will also give them to you now…

  8. “the derivative of f with respect to x” Y prime “the derivative of y with respect to x” “the derivative of f with respect to x” “the derivative of f of x”

  9. Note: dx does not mean d times x ! dy does not mean d times y !

  10. does not mean ! does not mean ! Note: (except when it is convenient to think of it as division.) (except when it is convenient to think of it as division.)

  11. Example • Use the definition to find the derivative of at a=1. • Answer:

  12. Graphing f’(x) • To graph the derivative, estimate the slope at a few points, then plot those values on the new graph.

  13. Example

  14. When can you not find the derivative? • Differentiability implies continuity! If a function is not continuous, it is not differentiable. • Cusps/points, vertical asymptotes, jumps/gaps

  15. Homework

More Related