Question

I have to determine the price that needs to be charged to obtain the largest revenue.

q=-p^2+33p+9 so
R=p(-p^2+33p+9) or =-p^3+33p^2+9p
I then need to take the derivative
R'=-3p^2+66p+9
Now I somehow need to solve for p to determine my price to obtain my largest revenue. How do I do this.

Answer 1

To find a maximum, set your marginal revenue (R') equal to zero. Now then, R' is a quadradic equation. So, use the quadradic formula.
-b +- sqrt(b^2+4ac) / 2a

Answer 2

my bad. it's -4ac in the quadradic, not +4ac