You are here:

Calculus/continuous function

Advertisement

Expert: Alon Mandes - 11/17/2008


Question
I have function  f(x)  which is continuous and nonnegative.
Is it possible to show (to prove) that:

max f(x) < f(x_0) ( where max f(x) is calculate over the interval |x-x_0| > delta )
implies
|x-x_0| < delta ?

Thanks in advance.

Answer
For every continuous nonnegative function f(x), in the interval
[a,b], always max{f(x)} ≥ f(xo) where xo Є [a,b]. "belongs to".
Max{f(x)}=f(xo), when xo is local max. & this statement holds good
regardless if |x-xo|<δ or |x-xo|>δ . & max{f(x)} can never
be < f(xo), if xo Є [a,b].

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.