Concept explainers
One-sided derivatives The right-sided and left-sided derivatives of a function at a point a are given by
respectively, provided these limits exist. The derivative f′(a) exists if and only if f+′(a) = f−′(a).
- a. Sketch the following functions.
- b. Compute f+′(a) and f−′(a) at the given point a.
- c. Is f continuous at a? Is f
differentiable at a?
31. f(x) = |x − 2|; a = 2
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage