My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 17th, 2017, 03:45 PM   #1
Member
 
Joined: May 2017
From: France

Posts: 50
Thanks: 1

A strange Inequality

Hi,

Let $\displaystyle g\in C^1([0,1],\mathbb R)$
Is it true that : $\displaystyle 4\times (\max(g)-\min(g))\geq \min(g')$ ?

Cordially.
Dattier is offline  
 
June 27th, 2017, 05:52 AM   #2
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,079
Thanks: 87

It seems to work if you sketch out a few representative curves. From there you could probably develop a proof if you're interested beyond the "gotcha" phase.
zylo is offline  
June 27th, 2017, 05:57 AM   #3
Member
 
Joined: May 2017
From: France

Posts: 50
Thanks: 1

Gotcha
Dattier is offline  
June 27th, 2017, 06:48 AM   #4
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,079
Thanks: 87

Quote:
Originally Posted by Dattier View Post
Gotcha
You forgot "Cordially"
zylo is offline  
June 27th, 2017, 06:51 AM   #5
Member
 
Joined: May 2017
From: France

Posts: 50
Thanks: 1

Gotcha
Dattier is offline  
June 27th, 2017, 07:00 AM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,854
Thanks: 2228

Math Focus: Mainly analysis and algebra
I may have misunderstood, but $$g:[0,1]\mapsto \mathbb R \quad \text{$g,g'$
continuous}$$
Has a maximum value for $\min{(g')}$ of $\max{(g)} - \min{(g)}$. This when $\min{(g)}=g(0)$, $\max{(g)}=g(1)$ and $g$ is a straight line.

If I haven't understood, the question seems trivial. What have I got wrong?

Last edited by v8archie; June 27th, 2017 at 07:02 AM.
v8archie is online now  
June 27th, 2017, 07:19 AM   #7
Member
 
Joined: May 2017
From: France

Posts: 50
Thanks: 1

Are you say : $\displaystyle \max(g)-\min(g) \geq \min(g')$ ?

What about $\displaystyle g(x)=\sinh(x)$ ?
Dattier is offline  
June 27th, 2017, 08:33 AM   #8
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,854
Thanks: 2228

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by Dattier View Post
Are you say : $\displaystyle \max(g)-\min(g) \geq \min(g')$ ?
I believe so.

$\sinh 1 - \sinh 0 \approx 1.18 - 0 = 1.18$
$\min{(\cosh x)}=1$

Last edited by v8archie; June 27th, 2017 at 08:36 AM.
v8archie is online now  
June 27th, 2017, 09:05 AM   #9
Member
 
Joined: May 2017
From: France

Posts: 50
Thanks: 1

edit : I must think

What about this inequality $\displaystyle 4(\max(g)-\min(g))\geq \min(g'')$, when $\displaystyle g \in C^2([0,1])$

Last edited by Dattier; June 27th, 2017 at 09:16 AM.
Dattier is offline  
June 27th, 2017, 09:27 AM   #10
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,854
Thanks: 2228

Math Focus: Mainly analysis and algebra
That sounds plausible. Again consider the case where $g''$ is constant (giving the maximum value for $\min{(g'')}$.
v8archie is online now  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
inegality, inequality, strange



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
A strange integral sg555 Calculus 3 April 11th, 2016 10:29 PM
Strange Inequality vlagluz Number Theory 5 January 7th, 2015 03:18 AM
strange probability phillip1882 Advanced Statistics 1 June 12th, 2013 11:14 AM
strange sum capea Real Analysis 0 September 29th, 2011 11:12 AM
the strange set bigli Real Analysis 3 May 27th, 2007 03:31 PM





Copyright © 2017 My Math Forum. All rights reserved.