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Derivative problem

See the attached files.

C(q) = 0.000002q^3 - o.o117q^2 + 84.446q + 23879
R(q) = -0.00003 * q^3 +0.0495q^2 + 118.02q
P(q) = -0.000032q^3 + 0.0612q^2 + 33.554q - 23879

Use the Cost, Revenue, and Profit functions to find. a) C`(q) b) R`(q) c) P`(q) Do these equations predict the quantity needed to maximize profit, and the amount? Explain your answer fully. (Please see Lab5student (attached) for information associated with answering my problem, which is lab 6, also attached). Thank you.

I found the derivatives :
C`(q)= .000006q^2 - .0234q + 84.446
R`(q)= -.00009q^2 + .099q + 118.02
P`(q)= -.000096q^2 + .1224q + 33.554

But, I don't know where to go from here. Do I set C'(q) = R'(q) to get max profit? I don't understand how to do the second part of the question, even assuming that I found the derivatives correctly.


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The slope of the tangential line to the profit function at the maximum point is ...

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This solution is comprised of a detailed explanation to solve derivative problem.