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:
 $AVR = \frac{f(x2) - f(x1)}{x2-x1}$
 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:
 $AVR = \frac{-8 - 16}{5-1}$
 $AVR = \frac{-24}{4}$
 $AVR = -6$
 Answer:
 the average rate of change in f(x) over the interval [1,5] is:
 $AVR = -6$