i need some math help

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=-3x^2+346x-3557

Answer 1

y= -3x^2 +346x -3557

take the derivative and set =0

y' =-6x +346 = 0

x = 346/6 =173/3 = 57 2/3 = profit maximizing sales level

plug into the original equation to solve for max profit

y =-3(173/3)^2 +346(173/3) - 3557

= -173^2/3 +346(173/3) -3557

= 173^2/3 -3557

= $6,419.33 = max profit

= $6419 to the nearest dollar