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

  • Thread starter renjean
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  • #1
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Homework Statement



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


Homework Equations


my gut instinct is that this is false.


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?
 

Answers and Replies

  • #2
382
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Hint: (f-1)'=1/f'(f-1(x))

What happens if f'(y)=0.
 
  • #3
7
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ah! that helps a lot. thanks for the hint!
 

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