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The total profit \( P(x) \) (in thousands of dollars) from a sale of \( x \) thousand units of a n ...
The total profit \( P(x) \) (in thousands of dollars) from a sale of \( x \) thousand units of a new product is given by \( P(x)=\ln \left(-x^{3}+9 x^{2}+21 x+1\right)(0 \leq x \leq 10) \). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit?