1 / 7

3.2 Differentiability

3.2 Differentiability. Differentiability. A function is differentiable at point c if and only if the derivative from the left of c equals the derivative from the right of c . AND if c is in the domain of f’. Differentiability. Find the derivative of at x = 0.

shawn
Download Presentation

3.2 Differentiability

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. 3.2 Differentiability

  2. Differentiability • A function is differentiable at point c if and only if the derivative from the left of c equals the derivative from the right of c. AND if c is in the domain of f’.

  3. Differentiability • Find the derivative of at x = 0. f is not differentiable at 0.

  4. DIFFERENTIABILITY • A function is differentiable if it has a derivative everywhere in its domain. It must be continuous and smooth. • No “sudden change” in slope.

  5. DIFFERENTIABILITY • Derivatives will fail to exist at: corner vertical tangent any discontinuity cusp

  6. Using the calculator • The numerical derivative of f at a point a can be found using NDER on the calculator. • Syntax: NDER (f(x), a) • Note: The calculator uses h = 0.001 to compute the numerical derivative, so it is a close approximation to the actual derivative. • Example:Compute NDER of f(x) = x3at x = 2.

  7. differentiability • THEOREM: • If f has a derivative at x = a, then f is continuous at x = a. Differentiability implies continuity.

More Related