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**mathcalculushelp** Revenue for sales of rubber baby-buggy bumpers is given by

R(q)=90q^2-q^3 for 0__<__q__<__70 .

a.what is the maximum revenue?

b.at what quantity is revenue increasing the fastest?

I tried finding R'(q)=180q-3q^2

and then from here found out p=-b/2a so that price(p) is set in R'(p) to find the maximum revenue.

180q - 3q^2 = 0

3q(60 - q) = 0

q = 0 , q = 60 ... which value of q maximizes R ?

once you determine that fact, find R(q) for that value.

I am not quite sure what part b wants.Am I doing part a correct?Any help?

the question is asking for the value of q for which R'(q) is a maximum ...

R''(q) = 180 - 6q = 0

q = 30 ... will this value of q yield a maximum for R'(q) ?

how can you tell?