ahem I know about e^-x^ and convergence thanks, I had some math in high school too.

I don't know what it means for the tendency of the rate of profit to be negative (or positive, or 0 for that matter). It's not a number. If you're talking about the rate of profit of course that can go negative. I think what you mean is that it will be balanced out, but not as high as it was before. Here is how its explained in Wage labour and capital, emphasis mine

We have just seen how the fluctuation of supply and demand always bring the price of a commodity back to its cost of production. The actual price of a commodity, indeed, stands always above or below the cost of production; but the rise and fall reciprocally balance each other, so that, within a certain period of time, if the ebbs and flows of the industry are reckoned up together, the commodities will be exchanged for one another in accordance with their cost of production. Their price is thus determined by their cost of production.

If you want to illustrate this movement a function like cos(x)/x would be more prudent. Here is 10*cos(x)/x to make it "pop" more:

Remember that convergence doesn't necessarily mean monotone convergence, and you'll be hard pressed to find a monotone graph in economics 😄 Here is a more illustrive graph for TRPF

You also say that "companies continue to produce stuff as long as the profit is larger than zero, which it always stays" which is absolutely false! A companies profit absolutely can be zero, or even negative! Remember profit = m - m', where m' is the money you have after selling the commodity. Or in more plain words, if you have less money after selling than before producing you made negative profit. If you didn't get your investment back, you didn't make profit.

Ok so unprofitable businesses keep going bankrupt, get gobbled up by a bigger corporation until one corporation has a monopoly. That's the trend we're seeing right? How many corporations for food are there left now? Nestle, Unilever, Coca Cola, Mondelez and that's pretty much it right? Well what happens when the tendency of the rate of the profit to fall forces them to no longer produce food. Do we just go extinct?

This (in case of the "butter mountains" and in general) isn't some politicians deciding which companies to keep, this is the state intervening to save itself. They have to prop up an entire industry that cannot reduce costs any further which means that the price keeps fluctuating around 0 profit which means the entire industry goes extinct. That's why there is a fixed price on milk, not to save some companies, but to prop up the entire industry. Capitalism will devolve sooner or later into state planning since without this state intervention industries start collapsing.

Could you imagine the ramification of the entire dairy industry dying out? (😸) The economy would go haywire, entire villages depend on their dairy farming, they would revolt it would be pandemonium. This is where capitalism finally leads.