PPT-Differentiability

Chapter 32 How Might Fail to Exist   A function will not have a derivative at a point where the slopes of the secant lines fail to approach a limit as Some of the common ways where a function fails to have a derivative.
(iii) Gateaux Differentiable
(ii) All Directional Derivatives Exist
(i) Partial Derivatives Exist However, the converses of the above three implications are not true. Below are counterexample 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 . Objective: Understand the relationship between differentiability and continuity. Miss . Battaglia. BC Calculus. Differentiability & Continuity. Alternative limit form of the derivative:. provided this limit exists. Note the limit in this alternative form requires that the one-sided limits. isdifferentiableinnormat,thatis,ifthereexistsavectorfunctionsinsuchthattheHellingerderivativeatInparticular,ifforafamilyofprobabilitymeasures,saythatisHellingerdifferentiableatisHellingerdifferentiabl c x = , the function must be continuous, and we will then see if it is differentiable. Let Section 3.2a. A function will not have a derivative at a point . P . (. a. , . f. (. a. )) where. the slopes of the secant lines,. How . f. (. a. ) Might Fail to Exist. f. ail to approach a limit as . 1980 . AB Free Response 3. Continuity and Differentiability of Inverses. If . f. . is continuous in its domain, then its inverse is continuous on its domain. . If . f. . is increasing on its domain, then its inverse is increasing on its domain . are . Continuous. Connecting Differentiability . and . Continuity. Differentiability and Continuity. Continuous functions . are . not necessarily differentiable. . For instance, start with . ves. By: Sameer, Snigdha, Aditya. Limits. Recall that…. A limit is when a function gets super close to a number from both sides of x, but the function never reaches that number…. It’s predicting a number between two neighboring points..