Maximizing Profit: Supppose r(X) = X^2/(x^2+1) represents revenue and c(X)= (x-1)^3/3 – 1/3 represents cost, with X measured in thousands of units. Is there a production level that maximizes profit? If so, what is it?

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Maximizing Profit: Supppose r(X) = X^2/(x^2+1) represents revenue and c(X)= (x-1)^3/3 – 1/3 represents cost, with X measured in thousands of units. Is there a production level that maximizes profit? If so, what is it?

Mathematics
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Take r(x) - c(x) = p(x) .. Now apply maxima minima to p(x)
That's where i have trouble, subtracting (x^2/(x^2+1) - (x-1)^3/3 – 1/3. After that I know I find the derivative and set it to zero to find the critical points.

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