Find the maximum profit that a company can make, if the profit function isgiven by `p(x)=41-24 x-18 x^2`

Explanation

Given profit function:
`p(x) = 41 - 72x-18x^(2)`
` rArr p'(x) =- 72 - 36x=-36 (2+x)`
and ` p''(x) =- 36`
and again differentiating w.r.t. x,p''(x) =- 36
For maxima/minima, p'(x) = 0 ltbr. ` rArr -36 (2+x)=0`
` rArr x+2 = 0 rArr x =- 2`
at ` x=- 2, p''(-2) =- 36 lt 0`
` :. ` at x =- 2, function is maximum.
and maximum profit = `p(-2) = 41 -72(-2) - 18 (-2)^(2) = 41 + 144-72 = Rs. 113`.