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

[renjean]

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?

 

[deluks917]

Hint: (f^-1)'=1/f'(f^-1(x))

What happens if f'(y)=0.

 

[renjean]

ah! that helps a lot. thanks for the hint!