1 / 7

Section 2.2

Section 2.2. Differentiability. Ways a function might not be differentiable. 1. a corner Often occurs with absolute value functions. Ways a function might not be differentiable. 2. A cusp. Often seen when a function has a rational exponent… x 2/3.

cromer
Download Presentation

Section 2.2

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. Section 2.2 Differentiability

  2. Ways a function might not be differentiable. • 1. a corner • Often occurs with absolute value functions.

  3. Ways a function might not be differentiable. • 2. A cusp. • Often seen when a function has a rational exponent… x2/3.

  4. Ways a function might not be differentiable. • 3. A vertical tangent. • Example: Cube root function.

  5. Ways a function might not be differentiable. • 4. A discontinuity.

  6. Differentiable vs. Continuous • Differentiability implies local linearity. • A function starts to look like its tangent line when you zoom in very close. • If a function is differentiable, then it is continuous. The converse, however, is not necessarily true.

  7. Derivatives on the Calculator • Math – 8 (nderiv) • Tell the calculator the variable, the function, and the value at which you are evaluating the derivative. You can enter x=x instead of a value if you want to graph the derivative.

More Related