MathematicalAnalysis Suppose f (x) is defned on (a, b) and continuous at c, where a 0, f (c) < 0, and f (c) = 0 separately.) (b) Is the condition that f is continuous at c necessary in (a)? Justify your answer.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
icon
Related questions
Question
MathematicalAnalysis
Suppose f (x) is defned on (a, b) and continuous
at c, where a <c< b.
(a) Prove that if |f | is differentiable at c, then f is
differentiable at c. (Hint: Consider the cases f (c)
> 0, f (c) < 0, and f (c) = 0 separately.)
(b) Is the condition that f is continuous at c
necessary in (a)? Justify your answer.
Transcribed Image Text:MathematicalAnalysis Suppose f (x) is defned on (a, b) and continuous at c, where a <c< b. (a) Prove that if |f | is differentiable at c, then f is differentiable at c. (Hint: Consider the cases f (c) > 0, f (c) < 0, and f (c) = 0 separately.) (b) Is the condition that f is continuous at c necessary in (a)? Justify your answer.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax