Suppose we have a postiive, differentiable function $\displaystyle f$ such that |f'(x)| <= f(x) for any x.
Prove that the integral from $\displaystyle 1\to \infty$ of $\displaystyle f$ converges iff the sum from $\displaystyle 1 \to n$ of f(n) converges
2. Sorry I should have added that a hint was to use legrange to show that for every $\displaystyle n$, and every $\displaystyle x$ in [n,n+1], f(n)/10 <= f(x) <= 10f(n)