microeconmics: can a monopolistic firm be profitable if its marginal revenue is negative? Statement: If a monopoly is producing a quantity for which its MR is negative, its total profit cannot be positive.

Is this statement correct or incorrect, and why?

I've read a lot about this, but sources tend to discuss maximizing profitability, while the question above presumes that MR &lt; 0 (and obviously smaller than MC) but wonders about profitability in this scenario.

My hunch is that yes, it is possible, but I'm struggling to prove it.

Edit: this getting downvoted is the reason why SE is deteriorating at the rate it is. I’ll go look for a more welcoming community.
As a counterexample to the statement, consider the following:

Let demand be $p=10-q$, so that $MR=10-2q$. Suppose there’s no cost, so that profit equals revenue. If the monopolist produces at $q=6$, $MR=-2&lt;0$, but $TR=(10-6)6=24&gt;0$, thus contradicting the statement.