Mean Value Theorem problem help

physicsman2

1. The problem statement, all variables and given/known data
A company introduces a new product for which the number of units sold S is
S(t)=200(5-(9/(2+t)) where t is the time in months

a) Find the average value of S(t) during the first year
b)During what month does S'(t) equal the average value during the first year

2. Relevant equations
f'(c)=(f(b)-f(a))/(b-a)

3. The attempt at a solution
well, i have no idea how to do it, but i believe for a), you have to find the derivative of the function(which i have no clue what it is) then use the equation given above to find the average value
For part b), i just have no clue

physicsman2

i think i got it but i just need some reinforcement on my answers

for a), you do (f(12)-f(1))/(12-1) using the original equation since the interval for months is [1,12] since i dont think zero would be in that kind of interval
then for b) you would set that answer equal to the derivative of the equation and solve for t

am i right

CompuChip

Homework Helper
Yes, although I suspect you start at t = 0.

For the derivative, I suggest working out the brackets and using the chain rule... do you know how to differentiate 1/u with respect to u?

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physicsman2

i already found the derivative but why would you start at t = 0 if there really is no 0 month if the first month is 1

physicsman2

can someone please tell me why t = 0 and not 1

mistermath

Sure, if you start at t = 1, then what about all that information from t = 0 to t = 1? (the first 30 days).

physicsman2

thanks it makes more sense

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