What is the average rate of change of f(x)=2x−1 over the interval 1≤x≤5 ?
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 by the difference in the x-values at the endpoints.
In this case, the function is f(x) = 2x - 1 and the interval is 1 ≤ x ≤ 5.
First, find the function values at the endpoints:
f(1) = 2(1) - 1 = 2 - 1 = 1
f(5) = 2(5) - 1 = 10 - 1 = 9
Next, find the difference in the function values:
f(5) - f(1) = 9 - 1 = 8
Then, find the difference in the x-values at the endpoints:
5 - 1 = 4
Finally, calculate the average rate of change:
Average rate of change = (f(5) - f(1))/(5 - 1)
Average rate of change = 8/4
Average rate of change = 2
Therefore, the average rate of change of f(x) = 2x - 1 over the interval 1 ≤ x ≤ 5 is 2.