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Find the maximum profit that a company can make, if the profit function is given by $ p(x) = 41 - 72x - 18x^2$

$\begin{array}{1 1} 59\\ 49 \\ 60 \\100 \end{array} $

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  • $\large\frac{d}{dx}$$(x^n)=nx^{n-1}$
Step 1:
For maxima and minima
Now $p'(x)=0$
$\Rightarrow 12(2+3x)=0$
Step 2:
$p'(x)$ changes sign from +ve to -ve.
$\Rightarrow p(x)$ has a maximum value at $x=\large\frac{-2}{3}$
Maximum profit=$p(\large\frac{-2}{3}\big)$
answered Aug 7, 2013 by sreemathi.v

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