Question

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

Answer 1

given, P(x) = 41 - 72x - 18x²
differentiate with respect to x ,
dP(x)/dx = 0 - 72 - 36x = -72 - 36x
now, put dP(x)/dx = 0 = -72 - 36x
x = -2

let's check , d²P(x)/dx² at x = -2
d²P(x)/dx² = -36 < 0
hence, P(x) will be maximum at x = -2
so, maximum value of P(x) = P(-2)
= 41 - 72(-2) - 18(-2)²
= 41 + 144 - 72
= 185 - 72
= 113

hence, maximum profit that a company can make is 113 units .

Answer 2

Answer:

Step-by-step explanation:

Hope you understood.