Answer:
The average rate of change of f(x) = x + 6 on [4,9] is 1.
Step-by-step explanation:
Given a function y, the average rate of change S of y=f(x) in an interval
will be given by the following equation:
![S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Bf%28x_%7Bf%7D%29%20-%20f%28x_%7Bs%7D%29%7D%7Bx_%7Bf%7D%20-%20x_%7Bs%7D%7D)
In this problem, we have that:
![f(x) = x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%20%2B%206)
Interval [4,9]. So
![x_{s} = 4, x_{f} = 9, f(x_{f}) = f(9) = 9+6 = 15, f(x_{s}) = f(4) = 4+6 = 10](https://tex.z-dn.net/?f=x_%7Bs%7D%20%3D%204%2C%20x_%7Bf%7D%20%3D%209%2C%20f%28x_%7Bf%7D%29%20%3D%20f%289%29%20%3D%209%2B6%20%3D%2015%2C%20f%28x_%7Bs%7D%29%20%3D%20f%284%29%20%3D%204%2B6%20%3D%2010)
![S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}} = \frac{15 - 10}{9 - 4} = 1](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Bf%28x_%7Bf%7D%29%20-%20f%28x_%7Bs%7D%29%7D%7Bx_%7Bf%7D%20-%20x_%7Bs%7D%7D%20%3D%20%5Cfrac%7B15%20-%2010%7D%7B9%20-%204%7D%20%3D%201)
The average rate of change of f(x) = x + 6 on [4,9] is 1.