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
In this figure, the graph crosses the x-axis at x = 0 and x = 6
This represents the profit is 0 when the price is $0 and $6, respectively
The maximum value
This represents the maximum profit that can be made.
From the graph, the maximum profit is $120
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 average rate of change
This is calculated as:
[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]
So, we have:
[tex]m = \frac{f(3) - f(1)}{3 - 1}[/tex]
[tex]m = \frac{f(3) - f(1)}{2}[/tex]
Substitute known values
[tex]m = \frac{120 - 60}{2}[/tex]
[tex]m = \frac{60}{2}[/tex]
Simplify
[tex]m = 30[/tex]
Hence, the average rate of change from x = 1 to x = 3 is a profit of $30 per unit sale
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