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

This function is a quadratic equation with a global maximum.

If you look carefully, the x-intercepts are x =10 and x = 200. Based on the characteristics of quadratic equation, the maximum lies in:

x = (10+200)/ 2 = 105

Then, you sub x = 105 into the equation, you will get the maximum profit:

f(105) = 18050