Question

Given f(x) =17 -x2 what is the average rate of change in f(x) over the interval [1,5]

Answer 1

By definition the average rate of change is given by:

`AVR = (f(x2) - f(x1))/(x2-x1)`
We have the following function:

`f(x) =17 - x^2`
We evaluate the function for the given interval:
For X = 1:

`f(1) =17 - 1^2`

`f(1) =17 - 1`

`f(1) =16`
For X = 5:

`f(5) =17 - 5^2`

`f(5) =17 - 25`

`f(5) =-8`
Then, replacing values we have:

`AVR = (-8 - 16)/(5-1)`

`AVR = (-24)/(4)`

`AVR = -6`
Answer:
the average rate of change in f(x) over the interval [1,5] is:

`AVR = -6`