Answer:
The average rate of change is 64
Step-by-step explanation:
Given
[tex]f(x) = 7x^2 - 6x + 6[/tex]
Required'
Average rate over 2 < x < 8
The average rate of change is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where a < x < b
So, we have:
[tex]Rate = \frac{f(8) - f(2)}{8-2}[/tex]
[tex]Rate = \frac{f(8) - f(2)}{6}[/tex]
Calculate f(8) and f(2)
[tex]f(x) = 7x^2 - 6x + 6[/tex]
[tex]f(8) = 7 * 8^2-6 * 8 +6 = 406[/tex]
[tex]f(2) = 7 * 2^2-6 * 2 +6 = 22[/tex]
So:
[tex]Rate = \frac{f(8) - f(2)}{6}[/tex]
[tex]Rate = \frac{406 - 22}{6}[/tex]
[tex]Rate = \frac{384}{6}[/tex]
[tex]Rate = 64[/tex]
