Final answer:
To find the average rate of change of a function over an interval, calculate the difference in function values at the endpoints and divide by the difference in x-values.
Step-by-step explanation:
To find the average rate of change of a function over an interval, you need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.
For the function f(x) = x³ - 5x + 7 over the given intervals:
i. [0, 50]
The rate of change is:
(f(50) - f(0))/(50 - 0)
Calculate the function values at x=0 and x=50, substitute the values in the formula, and simplify to find the answer.
ii. [50, 100]
The rate of change is:
(f(100) - f(50))/(100 - 50)
Repeat the steps above to find the rate of change over this interval.