email@example.com wrote in news:firstname.lastname@example.org:
> Suppose f:[0, oo) --> R is increasing, differentiable and has a finite > limit as x --> oo. Then, must we have lim x --> oo f'(x) = 0? I guess > not, but couldn't find a counter example. > > Thank you
Something like f(x) = sum_1^infinity arctan(2^n ( x-2^n) )/2^n should
work. f'(x) is a sum of terms like 1/(1 + (2^n x -2^(2n))^2. f'(2^n)=1 plus some small positive terms. But f'(2^n+2^(n-1)) should be pretty close to zero.