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 [tex]y=f(x)[/tex] in an interval [tex](x_{s}, x_{f})[/tex] will be given by the following equation:
[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}[/tex]
In this problem, we have that:
[tex]f(x) = x + 6[/tex]
Interval [4,9]
Continuous function(no denominator or even root), this is why i can consider 9 a part of the interval for the calculation. So
[tex]x_{s} = 4, x_{f} = 9, f(x_{s}) = f(4) = 10, f(x_{f}}) = f(9) = 15[/tex].
So
[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}} = \frac{15 - 10}{9 - 4} = 1[/tex]
The average rate of change of f(x) = x + 6 on [4,9) is 1.
