Question

Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?

Answer 1

The x intercept of the given graph of the company's profit is where the curve of the graph crosses the x-axis.

How to determine the x-intercept

From the figure, the graph crosses the x-axis at x values of 0 and 6

This represents the profit is 0 when the price is $0 and $6, respectively

The increasing and the decreasing interval

From the graph, the graph increases from x = 0 to x = x = 3, and it decreases from x = 3 to x = 6

These intervals represent when the profit increases, and when it decreases

The maximum value

This represents the maximum profit that can be made.

From the graph, the maximum profit is $120

The average rate of change

This is calculated as:

$m = \frac{f(b) - f(a)}{b - a}$

So, we have:

$m = \frac{f(3) - f(1)}{3 - 1}$

$m = \frac{f(3) - f(1)}{2}$

Substitute known values

$m = \frac{120 - 60}{2}$

$m = \frac{60}{2}$

Simplify

$m = 30$

Hence, the average rate of change from x = 1 to x = 3 is a profit of $30 per unit sale

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