By definition, the average rate of change is given by:
We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:
Evaluating for x = 3:
Then, the AVR is:
For f (x) = 3x - 8:
Evaluating for x =4:
Evaluating for x = 5:
Then, the AVR is:
For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:
Evaluating for x = 4:
Then, the AVR is:
For f (x) = x ^ 2 - 5:
Evaluating for x = -1:
Evaluating for x = 1:
Then, the AVR is:
Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]