Answer:
The average rate of change of the function in this interval is of 18.
Step-by-step explanation:
The average rate of change of a function [tex]f(x)[/tex] in an interval from a to b is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]f(x) = x^2 + 6x[/tex]
Where x goes from 5 to 7.
This means that [tex]b = 7, a = 5[/tex]. So
[tex]f(7) = 7^2 + 6(7) = 49 + 42 = 91[/tex]
[tex]f(5) = 5^2 + 6(5) = 25 + 30 = 55[/tex]
The rate of change is:
[tex]A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18[/tex]
The average rate of change of the function in this interval is of 18.
