Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
29. In Theorem 9.8, if f'(x o) = 0, no conclusion can be drawn about the equilibrium point xo of x' = f(x). Ex- plain this phenomenon by providing examples of equa- tions x = f (x) where (a) f' (xo) = 0 and xo is unstable, and (b) f' (xo) = 0 and xo is asymptotically stable.

29. In Theorem 9.8, if f'(x o) = 0, no conclusion can be drawn about the equilibrium point xo of x' = f(x). Ex- plain this phenomenon by providing examples of equa- tions x = f (x) where (a) f' (xo) = 0 and xo is unstable, and (b) f' (xo) = 0 and xo is asymptotically stable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x), where f is a differentiable function. 1. If f'(xo) < 0, then f is decreasing at xo and xo is asymptotically stable. 2. If f'(xo) - 0, then f is increasing at xo and xo is unstable. 3. If f'(xo) = 0, no conclusion can be drawn.
Transcribed Image Text:THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x), where f is a differentiable function. 1. If f'(xo) < 0, then f is decreasing at xo and xo is asymptotically stable. 2. If f'(xo) - 0, then f is increasing at xo and xo is unstable. 3. If f'(xo) = 0, no conclusion can be drawn.
29. In Theorem 9.8, if f' (x o) drawn about the equilibrium point xo of x' = ƒ(x). Ex- plain this phenomenon by providing examples of equa- tions x = f (x) where 0, no conclusion can be (a) f' (xo) = 0 and xo is unstable, and (b) f' (xo) = 0 and xo is asymptotically stable.
Transcribed Image Text:29. In Theorem 9.8, if f' (x o) drawn about the equilibrium point xo of x' = ƒ(x). Ex- plain this phenomenon by providing examples of equa- tions x = f (x) where 0, no conclusion can be (a) f' (xo) = 0 and xo is unstable, and (b) f' (xo) = 0 and xo is asymptotically stable.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
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,
SEE MORE TEXTBOOKS