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Analysis. Please check

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    If f is differentiable in an interval I and f' >0 throughout I, except possibly at a single point where f' >=0 then f is stictly incresing on I

    2. Relevant equations

    3. The attempt at a solution

    Ok what I have is I let f'(x) >0. I let a and b two points in the interval with a<b. then for some x in (a,b) with
    F'x= (f(b)-f(a))/b-a
    but f'(x)>0 for all x in (a,b) so
    (f(b)-f(a))/(b-a) >0

    since b-a>0 it follows that f(b)>f(a)

    What you can see I have proved that it is incresing in the interval but im not sure what to do when f'=0 any help would be much appreciated as I have been told that it is not fully correct.
  2. jcsd
  3. Feb 4, 2010 #2
    Do you have the integral and the fundamental theorem of calculus available to you, or only the derivative?
  4. Feb 4, 2010 #3
    Ah its cool. I managed to work it out. And im pretty convinced that it works.
    Thanks anyway appreciate it.
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