Exercise 5.2.5. Let fa(x) = { xa if x > 0 0 if x <0. (a) For which values of a is f continuous at zero? (b) For which values of a is ƒ differentiable at zero? In this case, is the derivative function continuous? (c) For which values of a is f twice-differentiable?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
icon
Related questions
Question

Please solve this as a Real Analysis problem, not a Calc 1 problem

Exercise 5.2.5. Let fa(x) = {
xa
if x > 0
0
if x <0.
(a) For which values of a is f continuous at zero?
(b) For which values of a is ƒ differentiable at zero? In this case, is the
derivative function continuous?
(c) For which values of a is f twice-differentiable?
Transcribed Image Text:Exercise 5.2.5. Let fa(x) = { xa if x > 0 0 if x <0. (a) For which values of a is f continuous at zero? (b) For which values of a is ƒ differentiable at zero? In this case, is the derivative function continuous? (c) For which values of a is f twice-differentiable?
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning