Respuesta :
The average rate of change of the function in the interval is of:
[tex]A = -\frac{1}{14(14 + h)}[/tex]
What is the average rate of change?
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this problem:
- The interval is [3, 3 + h], hence [tex]a = 3, b = 3 + h[/tex].
- [tex]f(3) = \frac{1}{3 + 11} = \frac{1}{14}[/tex]
- [tex]f(3 + h) = \frac{1}{3 + h + 11} = \frac{1}{14 + h}[/tex]
Then:
[tex]f(b) - f(a) = \frac{1}{14 + h} - \frac{1}{14} = \frac{14 - 14 - h}{14(14 + h)} = -\frac{h}{14(14 + h)}[/tex]
[tex]A = \frac{-\frac{h}{14(14 + h)}}{3 + h - 3} = -\frac{-\frac{h}{14(14 + h)}}{h} = -\frac{1}{14(14 + h)}[/tex]
You can learn more about the average rate of change at https://brainly.com/question/7501987
