Intervals?

Question

I really need help in math, can anyone please help me...

The revenue of Portside Fish Shanty, located at a popular summer resort, is approximately
R(t) = 2(5 -4 cos 6(π/6) t
;

where 0≤ t ≤12, t is measured in weeks with t = 1 corresponding to the first week of June, and R is measured in thousands of dollars.The cost function, over the same interval of time, is given by
C(t) = 1 + (2π/3) t ;

and it is also measured in thousands of dollars.

(a) Find the intervals of increase and decrease of R(t).
(b) Find the intervals of increase and decrease of C(t).
(c) Find the intervals of increase and decrease of the profit functionP(t).
(d) At what value of t is the prot maximized? What is this maximum profit? You must fully justify your answer .

For this question, part a, do i have to change the cos to a actual number so i can solve for the critial numbers?
and for this, there is only one critial number? So what to do with one critial number?

Thanks!

R(t) = 2[ 5 -4 cos 6(π/6) t ]
;

Answer 1

Unfortunately, you made one or more typos. For example, the definition of R has two left parentheses and one right parenthesis.

If R(t) = constant + constant * cos (constant * t), then it will have a maximum or minimum each time (constant*t) increments by pi. And the maxima and minimum will alternate in strict succession.

Naturally, when going from a minimum to a maximum the function is increasing, and the rest of the time it's decreasing.

Ah. The formula for C(t) is cleaner. Well, C is periodic, with period 3 weeks. So it will have a maximum every 3 weeks, then a minimum (also every 3 weeks) after each maximum.

What I just said basically takes care of a and b. c is harder, however. P(t) = constant + constant * cos(constant * t) + constant * cos (constant*t). So P'(t) = 0 + constant * sin (constant * t) + constant sin (constant * t). Now I wish you hadn't made the typos, because I can't help you in more detail without knowing what the correct expression for R(t) is.