Mean Value Theorem Word Problem - Larson Hoestetler

[shaggy22]

I'm not exactly sure when to take the derivative...

"A company introduces a new product for which the number of units sold S is given by S(t) = 200(5-(9/(2+t))) where t is the time in months

a) Find the average rate of change of S(t) during the first year

b) During what month does S'(t) equal its average rate of change?

For the first part do I use the Mean Value Theorem or do I just plug in 0 and 12 and divide by 12?

And is the second part it's just taking the derivative and setting it equal to part A right? I'm just not sure what to do for part A!

Thanks in advance

 

[pka]

\(\displaystyle \L \begin{array}{l}
S(t) = 200\left[ {5 - \left( {\frac{9}{{2 + t}}} \right)} \right] \\
S'(t) = \frac{{1800}}{{\left( {2 + t} \right)^2 }} \\
\frac{{1800}}{{\left( {2 + t} \right)^2 }} = \frac{{S(12) - S(0)}}{{12 - 0}} \\
\end{array}.\)

Now you need to solve for t to do part b.