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?

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?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 2E

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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?

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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