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Math Help - differentiability and extreme points question

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    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
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  4. #4
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    Re: differentiability and extreme points question

    Quote Originally Posted by transgalactic View Post
    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 .....
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  5. #5
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    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?
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