The function f(t) = 30 sin (pi over 3t) −15 models the temperature of a periodic chemical reaction where t represents time in hours. what are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take

F(t)=30 sin(pi/3 t)-15
when sin(pi/3 t) = 1, f(t) = 15 => max.
when sin(pi/3 t) = -1 f(t) = -45 .+ min.
period = 2π / (π/3) = 6 hrs.

Maximum value is maximum profit
The x intercepts are the prices that profit equals zero

B
Increasing from - infinity to 3 and decreasing from 3 to infinity. When price is less than 3 every increase in price results in an increase in profit. When price is greater than 3, every increase in price results in a decrease in profit. So what this is saying about sales is that when you set the price beyond 3 bucks, the amount of people willing the buy at that price drops such that you start making LESS profit because less people are willing to buy, and the lack of buyers offsets the additional price that the others are paying.

C
The average rate of change is 60 and this represents the increase in profit per increase in price