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

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

`((-b)/(2a),f((-b)/(2a)))`

From (1) and (2) we get

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

`(-b)/(2a)=(-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.