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Find the maximum profit that a company can make if the profit function is given by \[P(x)=41-24x-18x^2\]

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  • Necessary condition for maximum or minimum 'p' is $ \large\frac{dp}{dx}=0$
  • Condition for maximum is $ \large\frac{d^2p}{dx^2}$ is negative.
Step 1
$ \large\frac{dp}{dx}=-24-36x=0$
$ \Rightarrow x = - \large\frac{2}{3}$
Step 2
$ \large\frac{d^2p}{dx^2}=-36$ is negative
Step 3
maximum profit = $ p\bigg( \large\frac{-2}{3} \bigg) $$= 49$
answered Apr 11, 2013 by thanvigandhi_1
edited May 13, 2014 by balaji.thirumalai

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