Answer:
Since,



1) 
Differentiating with respect to x,

2) 
Differentiating w. r. t x,

3) 
Differentiating w. r. t. x,

4) 
Differentiating w. r. t. t,

5) 
Differentiating w. r. t. p,
6) 
Differentiating w. r. t. t,

7) 
Differentiating w. r. t. y,

Answer:
15 rubber bands per day
Step-by-step explanation:
Answer:
He should pay $2,790.7.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.
After t years, the total amount of money is:

In this question:
Rate of 10%, so I = 0.1.
9 months, so 
How much should he pay for a note that will be worth $3,000 in 9 months?
We have to find P for which T = 3000. So



Then





He should pay $2,790.7.

now, we get critical points from zeroing out the derivative, and also from zeroing out the denominator, but those at the denominator are critical points where the function is not differentiable, namely a sharp spike or cusp or an asymptote.
so, from zeroing out the derivative we get no critical points there, from the denominator we get x = 8, but can't use it because f(x) is undefined.
therefore, we settle for the endpoints, 4 and 6,
f(4) =3 and f(6) = 7
doing a first-derivative test, we see the slope just goes up at both points and in between, but the highest is f(6), so the absolute maximum is there, while we can take say f(4) as the only minimum and therefore the absolute minumum as well.