By definition the average rate of change is given by:
[tex]AVR = \frac{f(x2) - f(x1)}{x2-x1} [/tex]
We have the following function:
[tex]f(x) =17 - x^2[/tex]
We evaluate the function for the given interval:
For X = 1:
[tex]f(1) =17 - 1^2[/tex]
[tex]f(1) =17 - 1[/tex]
[tex]f(1) =16[/tex]
For X = 5:
[tex]f(5) =17 - 5^2[/tex]
[tex]f(5) =17 - 25[/tex]
[tex]f(5) =-8[/tex]
Then, replacing values we have:
[tex]AVR = \frac{-8 - 16}{5-1} [/tex]
[tex]AVR = \frac{-24}{4} [/tex]
[tex]AVR = -6 [/tex]
Answer:
the average rate of change in f(x) over the interval [1,5] is:
[tex]AVR = -6 [/tex]
