Find the maximum profit that a company can ma | vedclass

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(A) The profit function is given as $p(x) = 41 - 72x - 18x^{2}$.To find the maximum profit,we find the first derivative $p'(x)$:$p'(x) = \frac{d}{dx}(

Vedclass · Accepted Answer

$113$

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(A) The profit function is given as $p(x) = 41 - 72x - 18x^{2}$.To find the maximum profit,we find the first derivative $p'(x)$:$p'(x) = \frac{d}{dx}(41 - 72x - 18x^{2}) = -72 - 36x$.Set $p'(x) = 0$ to find the critical point:$-72 - 36x = 0 \Rightarrow 36x = -72 \Rightarrow x = -2$.Now,find the second derivative $p''(x)$ to check for maxima:$p''(x) = \frac{d}{dx}(-72 - 36x) = -36$.Since $p''(-2) = -36 Now,calculate the maximum profit by substituting $x = -2$ into $p(x)$:$p(-2) = 41 - 72(-2) - 18(-2)^{2}$$p(-2) = 41 + 144 - 18(4)$$p(-2) = 41 + 144 - 72$$p(-2) = 113$.Hence,the maximum profit is $113$ units.

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

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