# differentiability and extreme points question

• Sep 2nd 2011, 05:43 AM
transgalactic
differentiability and extreme points question
2.b)
f is continues in [0,1] and differentiable in (0,1)
f(0)=0 and for x\in(0,1) |f'(x)|<=|f(x)| and 0<a<1
prove:
(i)the set {|f(x)| : 0<=x<=a} has maximum
(ii)for every x\in(0,a] this innequality holds $\frac{f(x)}{x}\leq max{|f(x)|:0<=x<=a}$
(iii)f(x)=0 for $x\in[0,a]$
(iii)f(x)=0 for $x\in[0,1]$
in each of the following subquestion we can use the previosly proves subquestion.
• Sep 2nd 2011, 07:18 AM
HallsofIvy
Re: differentiability and extreme points question
Once again, you have posted what looks like a homework with no indication of your own attempt to solve it.
• Sep 2nd 2011, 07:35 AM
transgalactic
Re: differentiability and extreme points question
my thought on each one:
i was given continuety on closed section and deffentiabilty on open section
so i can use here mean value theory
rolls thery
and weirshtrass
etc...
regarding a :
in order to have maximum by weirshrass its continues on closed section so i have a maximum and minimum between
but the question asks for total maximum(dont know the proper term)
so i dont know what t do next
?

its not home work
it me trying to solve a test from previos semester to which i dont have an answer
so i ask for tip regarding each one to help me solve it
• Sep 2nd 2011, 03:25 PM
mr fantastic
Re: differentiability and extreme points question
Quote:

Originally Posted by transgalactic
my thought on each one:
i was given continuety on closed section and deffentiabilty on open section
so i can use here mean value theory
rolls thery
and weirshtrass
etc...
regarding a :
in order to have maximum by weirshrass its continues on closed section so i have a maximum and minimum between
but the question asks for total maximum(dont know the proper term)
so i dont know what t do next
?

its not home work
it me trying to solve a test from previos semester to which i dont have an answer
so i ask for tip regarding each one to help me solve it

It is not our job to provide solutions to tests, exams etc. from a previous semester. It is the job of your institute to provide the solutions. If they are unwilling to provide the solutions, there is probably a very good reason for that .....
• Sep 2nd 2011, 10:55 PM
transgalactic
Re: differentiability and extreme points question
i dont want you to write a full solution
only guidance.i have written above what i know about general ways
could you say in general what to do from here?