The average rate of change on interval [1, 6] is equal to 2.
An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a period of time (interval).
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by:
Average rate of change = [f(b) - f(a)]/(b - a)
For f(a), we have:
f(a) = f(1) = 1² - 5(1) + 8
f(1) = 1 - 5 + 8
f(1) = 4
For f(b), we have:
f(b) = f(6) = 6² - 5(6) + 8
f(6) = 36 - 30 + 8
f(6) = 14
Substituting the parameters into the formula, we have;
Average rate of change = [f(b) - f(a)]/(b - a)
Average rate of change = [14 - 4]/(6 - 1)
Average rate of change = 10/5
Average rate of change = 2
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