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I don't know, I have it written down what the formula is and all the variables are defined. Let me also clarify - this is the amount of profit taken each month (not the total profit for m months).
It remains to derive the formula for the sum of the series, you wrote that you do it easily - do it. Then take the derivative, equate it to zero...
In my notations, your formula for the current month's withdrawal looks like this: , for the amount in period t:, is exactly the same as the one I got above.
Consequently, breaking down the beast-like derivative of this function is as difficult as the one above.
I think you can try to pre-prologarithmize f and then look for its maximum... Maybe it will be easier that way.
avtomat:
And then, in the second step, open the valve that divides the flow into two parts. This will change the input flow.
You don't see the solution yet?
No, I don't know what you're thinking. Tell me.
There are some that even the Pythagorean theorem, as interpreted by them, can't be understood.
OFFTOP:
At school they gave the most succinct proof of Pythagoras' theorem.
Note, the basic simplest (non-standard) idea is p.2. No knowledge of properties of similar triangles is used, also no knowledge of trigonometry is needed to understand the existence of function f either. I.e. such a proof can be given in primary schools after well (not as usual) explaining to children what area is.
OFFTOP:
In school they gave the most succinct proof of Pythagoras' theorem.
In what grade?
The formula S = c^2 * f(alpha) is not obvious to a 7th grader. It is taking for granted that it kind of is.
Accordingly, breaking the beast-like derivative of this function is just as hard as the above one.
Is the whole process stuck with the derivative?
Is this function x0*k*(1-(1+q-k)^2)/(k-q)?
If so, it's like no problem, I've solved them easily, just need to remember a bit. The variable q?
in which class?
The formula S = c^2 * f(alpha) is not obvious to a 7th grader. It is taking for granted that it kind of is.
Almost any child who has been introduced to the concept of the area of a figure well enough to feel it will have little difficulty understanding the above proof.
If a child truly understands what area is, he understands the measure of it and also understands that the area of any figure can be expressed through its characteristics (in this case the hypotenuse and angle) that uniquely define the figure.
No knowledge of the properties of similar triangles and trigonometry is needed.
I was on a visit recently and saw two stone pyramids (similar to Egyptian pyramids). Took them in my hands and put them at their bases (they are slightly different in size):
And came up with another proof of Pythagoras' theorem (clear from the construction).
Integer:
Весь процесс уперся в производную?
Вот эта функция - x0*k*(1-(1+q-k)^2)/(k-q)?
Если это так, то это как бы не проблема, я их легко решал, только вспомнить надо немного. Переменная q?
No, the problem is the derivative of k from:
It has to be equated to zero and solved with respect to k.
I can't do it the smart way, so I'll make it simple:
Let's say there is 10,000 on the deposit at the beginning of the period. Each period we add 5% to the deposit and reinvest them to the deposit. Each period we are allowed to withdraw only 3%.
If you withdraw all 3% of your money each period, all we get more than 4k$ (and do not give a shit about the deposit), otherwise we get only 0.5k$ (but with much on the deposit).
Almost any child who has been introduced to the concept of the area of a figure well enough to feel it will have little difficulty understanding the above proof.
If a child truly understands what area is, he or she understands the measure of it and also understands that the area of any figure can be expressed through its characteristics (in this case the hypotenuse and the angle), which uniquely define the figure.
But it's not a rigorous proof.
I can't do it the smart way, so I'll make it simple:
That's why we need a general analytical solution, not to draw such tables, but to substitute two input values into a simple formula and get the answer.
That's the point, all the above is "it feels like that's how it's going to be". That "it can somehow be expressed through something".
But it's not a rigorous proof.
What kind of hard evidence is that?! It's obvious: