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]
