Answer:
[tex]A(x) = 243[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^3 - 9x[/tex]
[tex]Interval: (12,6)[/tex]
Required
Determine the average rate of change
Average rate is calculated as thus;
[tex]A(x) = \frac{f(b) - f(a)}{b - a}[/tex]
In this case; b = 12 and a = 6
Calculating f(12)
[tex]f(12) = 12^3 - 9 * 12[/tex]
[tex]f(12) = 1728 - 108[/tex]
[tex]f(12) = 1620[/tex]
Calculating f(6)
[tex]f(6) = 6^3 - 9 * 6[/tex]
[tex]f(6) = 216 - 54[/tex]
[tex]f(6) = 162[/tex]
Substitute 12 for b and 6 for a in [tex]A(x) = \frac{f(b) - f(a)}{b - a}[/tex]
[tex]A(x) = \frac{f(12) - f(6)}{12 - 6}[/tex]
Substitute values for f(6) and f(12)
[tex]A(x) = \frac{1620 - 162}{12 - 6}[/tex]
[tex]A(x) = \frac{1458}{ 6}[/tex]
[tex]A(x) = 243[/tex]
