Question

See attached question

Answer 1

something missing after the "suppose \(\lim_{x\to \infty}f'(x)\)

Answer 2

in the question

Answer 3

=0, sorry

Answer 4

i must be too tired to think, but if a function is nice and continuous like \(f\) isn't it more or less obvious that \(\lim_{x\to \infty}f(x)=\lim_{x\to \infty}f(x+1)\)?
graphs are the same just shifted one unit to the left

Answer 5

I got it just give me a sec to write it up.

Answer 6

i want to see it because i must be missing something

Answer 7

only way i see a connection to the derivative is to use
\[\frac{f(x+1)-f(x)}{x-1}\]