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Find the Maximum Profit that a Company Can Make, If the Profit Function is Given by P(X) = 41 − 72x − 18x2 - Mathematics

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x2

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Solution

The profit function is given as p(x) = 41 − 72x − 18x2.
∴ p'(x)=-72-36x

⇒x=-7236=-2
Also,
p''(-2)=-36<0
By second derivative test, x=-2 is the point of local maxima of p.

∴ Maximum profit=p-2
                           =41-72(-2)-18(-2)2=41+144-72=113

Hence, the maximum profit that the company can make is 113 units.

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 6 | Page 232
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