Help Me with this question please

Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.

y=−9x^2+571x−3884

Answer 1

if y= profit, take the derivative and set = zero, solve for x, and plug that value back into the original equation

y' = -18x +571 = 0

18x = 571

x = 571/18 = 31.7

y =-9(31.7)^2 + 571(31.7) - 3884 = -9056,7 + 18100 -3884 = $5160 max profit