Question

The function f(x) = –2(x – 10)(x – 200) represents a company's monthly profit as a function of the number of items sold, x. What is the maximum monthly profit?

Answer 1

$18050 Is your answer

Explanation:

Answer 2

expand
f(x)=-2x^2+420x-4000
in form
f(x)=ax^2+bx+c
vertex (highest or lowest point, depending on graph)
vertex is -b/2a that is the x value
to find the profit, plug that x value back in

f(x)=-2x^2+420x-4000
-b/2a=-420/(2)(-2)=-420/-4=105

x min valu is 105
input to find profit
f(105)=-2(105-10)(105-200)
f(105)=-2(95)(-95)
f(105)=18050

max profit is $18050