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

what you do first is you times the F which will equal -2 which will give you an answer then you subtract that answer by 10 * by 200 than you have your answer

Answer 2

Answer:

The maximum monthly profit is 18050.

Step-by-step explanation:

The given function is

$f(x)=-2(x-10)(x-200)$

$f(x)=(-2x+20)(x-200)$

$f(x)=-2x(x-200)+20(x-200)$

$f(x)=-2x^2+400x+20x-4000$

$f(x)=-2x^2+420x-4000$              .... (1)

The vertex of a quadratic function  

$g(x)=ax^2+bx+c$          ..... (2)

is defend as

$(\frac{-b}{2a},f(\frac{-b}{2a}))$

From (1) and (2) we get

$a=-2,b=420,c=-4000$

$\frac{-b}{2a}=\frac{-420}{2(-2)}=105$

Put x=105 in the given function.

$f(105)=-2(105-10)(105-200)$

$f(105)=-2(95)(-95)$

$f(105)=18050$

Therefore the maximum monthly profit is 18050.