Find the maximum profit that a company can make, if the profit function is given by p (x) = 41 + 24x – 18x².

Solution

Here, $straight p left parenthesis straight x right parenthesis space equals space 41 plus 24 straight x minus 18 straight x squared$ $rightwards double arrow space space space space space straight p apostrophe left parenthesis straight x right parenthesis space equals 24 minus 26 space straight x$
$straight p apostrophe apostrophe left parenthesis straight x right parenthesis space equals space minus 36$
$At space space space straight x space equals space 2 over 3 comma space space space straight p apostrophe apostrophe left parenthesis straight x right parenthesis space equals space minus 36 space greater than space 0 space space space space rightwards double arrow space space space space straight p left parenthesis straight x right parenthesis space has space local space maximum space at space straight x space equals space 2 over 3 But space straight p left parenthesis straight x right parenthesis space has space one space extreme space point space straight x space equals space 2 over 3 space space space space rightwards double arrow space space space straight p left parenthesis straight x right parenthesis space has space local space maximum space when space straight x space equals space 2 over 3 and space maximum space profit space space equals space 41 plus 24 space open parentheses 2 over 3 close parentheses minus 18 space open parentheses 2 over 3 close parentheses squared space equals space 41 plus 16 minus 8 space equals space 49$

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Application Of Derivatives

Find the maximum profit that a company can make, if the profit function is given by p (x) = 41 + 24x – 18x².

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Find the maximum profit that a company can make, if the profit function is given by p (x) = 41 + 24x – 18x2.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the maximum profit that a company can make, if the profit function is given by p (x) = 41 + 24x – 18x².