Question

The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, being sold by the company: graph of quadratic function f of x having x intercepts at ordered pairs negative 0, 0 and 10, 0. The vertex is at 5, 160 Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent?

Answer 1

if profit = f(x) then the x-intercepts represent the points at which profit = 0 for price x

maximum f(x) = maximum profit

Answer 2

for intervals of increase/decrease, the function is increasing between 0 and the vertex, and decreasing between the vertex and 10

Answer 3

as for what that means, think about what f(x) represents

Answer 4

avg. rate of change formula = [f(x_2)-f(x_1)]/(x2-x1) where x1 = 2 and x2 = 5