This question is rather of economical nature. Let's say we have a function $f(x)$ that describes the result of some action depending on the amount of resource used $x$, for example:
$$f(x)=\frac{300}{100+x}$$
The smaller the result, the better!
EDIT: Consider the interval $0\leq x\leq 200$ for realistic $x$ values.
How would I determine, at which point the improvement becomes not worth the investment of more resource anymore? Is there any information missing, or can this be determined from the curve as it is?
You are missing some information to get an economically justifiable answer. Recall that Pareto efficiency in resource allocation occurs when the marginal cost of using the resource equals the marginal benefit.
In particular, I must assume that $f$ represents the benefit curve, and that the marginal benefit is given by the derivative of $f$.
There is no unique answer to this question without a cost curve. Well, there sort of is an answer, but it implicitly assumes that there is no cost associated with using the resource. In which case you would use as much of the resource as you could, since all consumption would improve your welfare at no cost.
Another option would be to assume that the cost of using $x$ resources would be $x$. Then the marginal cost is $1$, and you would solve for $x$ in $f'(x) = 1$. This does represent a relatively sensible cost curve, but it does not have increasing marginal costs, as most real cost curves do.
Actually, since, as you note in the comments, the marginal benefit $f'$ is always negative, you would never want to enter into the transaction. That is, $x$ is always $0$.