Proof involving limit of derivative

[ptolema]

Homework Statement

give an example of a function f for which lim f(x) as x\rightarrow\infty exists, but lim f'(x) as x\rightarrow\infty does not exist.

Homework Equations

f'(x) = lim [f(x+h)-f(x)]/h as h\rightarrow0

The Attempt at a Solution

for some reason, i can only seem to find equations where lim f(x) as x\rightarrow\infty does not exist, but lim f'(x) as x\rightarrow\infty does exist. ex.f(x)=x and f'(x)=1

 

[Coto]

Try thinking of functions that require the chain rule to find the derivative.
i.e. Let f(x) = g(h(x)). Then f'(x) = g'(h(x)) \cdot h'(x).