Answer:Part A) see the explanation
Part B) see the explanation
Step-by-step explanation:
The picture of the question in the attached figure
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?
Let
x ----> the price of pencils in dollars
f(x) ----> a company's profit in dollars
we know that
The function f(x) is a quadratic function having x-intercepts at (0,0) and (10,0)
The x intercepts give us the price when profit is zero, so the x-intercepts represent break-even points
The vertex is at (5,160)
f(x) represent a vertical parabola open downward
The vertex is a maximum
The x-coordinate of the vertex represent the price of the pencils when the value of the profit is maximum
The y-coordinate of the vertex represent the maximum profit
therefore
The maximum profit of $160 is when the price of the pencils is $5
Profit is increasing on the interval (0,5) and decreasing on the interval (5,10)
This represents that profit is increasing when selling price ranges from 0 dollars to 5 dollars, then decreases when selling price is 5 dollars to 10 dollars
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?
Find the average rate of change of the graph from x = 2 to x = 5
To find the average rate of change, we divide
Step-by-step explanation:
