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Limits of a function's derivative and how it relates to a function.

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove or disprove: if lim x->b (from the left) f'(x) = infinity then lim x->b (from the left) f(x) = infinity


    2. Relevant equations
    my gut instinct is that this is false.


    3. The attempt at a solution
    I have thought of many counterexamples but none of them seem to work. Does it matter that the limit is at a point and not as x-> infinity?
     
  2. jcsd
  3. Nov 15, 2011 #2
    Hint: (f-1)'=1/f'(f-1(x))

    What happens if f'(y)=0.
     
  4. Nov 16, 2011 #3
    ah! that helps a lot. thanks for the hint!
     
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