[Math] maximized profit w/ a cost & demand function

Question

I'm having trouble with this problem:

If

$C(x) = 14000 + 500x − 4.8x^2 + 0.004x^3$

is the cost function and

$p(x) = 4100 − 9x$

is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

I think that in order to find the answer, I have to find the derivatives of both the equations and set them equal to each other. However, I am getting multiple roots and none of the roots are the answers. What should I be looking for if not the roots?

Answer 1

The revenue is $x\cdot p(x)$. If you take the derivative of that and set it equal to the derivative of cost, I find a single positive solution.