2. A function f A → R is Lip- schitz if there exists an M> 0 so that for all x, y E A with x y we have f(x)-f(y)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
2.
A function f A → R is Lip-
schitz if there exists an M> 0 so that for all x, y E A with x y we
have
| f(x) = f(y) |
x-y
≤M.
Suppose that f [a, b] → R is differentiable and that f' is continuous on
[a, b]. Prove that f is Lipschitz.
Transcribed Image Text:2. A function f A → R is Lip- schitz if there exists an M> 0 so that for all x, y E A with x y we have | f(x) = f(y) | x-y ≤M. Suppose that f [a, b] → R is differentiable and that f' is continuous on [a, b]. Prove that f is Lipschitz.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,