This preview shows pages 1–12. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: = ( ) 1, 1, U x x x = < Thm. 2.1 Differentiability Implies Continuity If f is differentiable at x = c, then f is continuous at x = c. It is possible for a function to be continuous at x = c and not be differentiable at x = c. Thus, continuity does not imply differentiability. OneSided Derivatives l A function y = f(x) is differentiable on a closed interval [a, b] if it has a derivative at every interior point of the interval, and if the limits exist at the endpoints. l The usual relationship between onesided and twosided limits holds for derivatives. A function has a (twosided) derivative at a point iff the functions righthand and lefthand derivatives are defined and equal at that point. Joke Time What would America be called if we all drove pink cars? A pink carnation! Why should you never play cards in the jungle? Its full of cheetahs!...
View
Full
Document
This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.
 Fall '08
 JARVIS
 Calculus, Derivative

Click to edit the document details