1 / 14

Implicitly Defined Functions

Implicitly Defined Functions. Explicitly Defined Function. Implicitly Defined Equation. Implicitly Defined Functions. Implicit Differentiation Process. Example Implicitly Defined Functions. This is not a function, but it would still be nice to be able to find the slope.

warrent
Télécharger la présentation

Implicitly Defined Functions

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. Implicitly Defined Functions

  2. Explicitly Defined Function

  3. Implicitly Defined Equation

  4. Implicitly Defined Functions

  5. Implicit Differentiation Process

  6. Example Implicitly Defined Functions

  7. This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

  8. This can’t be solved for y.

  9. We need the slope. Since we can’t solve for y, we use implicit differentiation to solve for . Find the equations of the lines tangent and normal to the curve at . Note product rule.

  10. Find the equations of the lines tangent and normal to the curve at . tangent: normal:

  11. Example Derivatives of a Higher Order

  12. Find if . Higher Order Derivatives

  13. Examples

More Related