Final answer:
The average rate of change of the function f(x)=x²-1 over the interval [1,6] is calculated by subtracting the value at x=1 from the value at x=6 and then dividing by the length of the interval, which results in an average rate of change of 7.
Step-by-step explanation:
The average rate of change of a function over an interval [a, b] is calculated by subtracting the value of the function at a from the value of the function at b, and then dividing by the difference between b and a. So, for the function f(x)=x²-1, first find the value of the function at the endpoints of the interval [1, 6]: f(1) = 1² -1 = 0 and f(6) = 6² - 1 = 35. Then, compute the average rate of change as follows:
Average rate of change = [ f(b) - f(a) ] / [ b - a ]
= [ f(6) - f(1) ] / [ 6 - 1 ]
= [ 35 - 0 ] / [ 5 ]
= 35 / 5
= 7
Therefore, the average rate of change of f over the interval [1, 6] is 7.