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Find the derivative
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- In a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.Where does f(x) = x^3 / (x^2−1) have a critical point, which is not an extremum?Where does the function f(x,y)=3 − 10x + 12y − 5x2 − 6y2 have a critical point?