Question

The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:

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 the approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?

Answer 1

Question
(08.01, 08.04 MC) The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the

Answer 2

Part A:

1) X-intercepts: The x-intercepts represent the points where the profit function equals zero. In other words, these are the prices of erasers at which the company breaks even. For example, if there is an x-intercept at x = 2, it means that the company does not make a profit on selling erasers at $2.

2) Maximum value: The maximum value of the graph represents the highest profit the company can make from selling erasers. It is the peak of the graph and usually occurs at a specific price point. For example, if the maximum value occurs at x = 3, it means that the company earns the highest profit when selling erasers at $3.

3) Increasing and decreasing intervals: The increasing intervals of the graph represent ranges of prices where the profit is increasing. In other words, as the price of erasers increases within the range, the profit of the company also increases. The decreasing intervals, on the other hand, represent ranges of prices where the profit is decreasing. As the price of erasers decreases within the range, the profit of the company also decreases. These intervals provide insights into how changes in price affect the profit of the company.

Part B:

The average rate of change (AROC) from x = 1 to x = 4 is calculated by finding the slope of the secant line that connects the points (1, f(1)) and (4, f(4)). To find the approximate AROC, we use the formula:

AROC = (f(4) - f(1))/(4 - 1).

The AROC represents the average rate at which the profit changes per unit change in price. In this case, it represents the average increase or decrease in profit for each additional dollar charged for an eraser.