Final answer:
To find the average rate of change of the function f(x) = x^2 - 4 over the interval [6, 6.25), we calculate the change in the function's values and divide it by the change in x. The average rate of change is 12.25.
Step-by-step explanation:
To find the average rate of change of the function f(x) = x^2 - 4 over the interval [6, 6.25), we need to calculate the change in the function's values and divide it by the change in x.
First, let's find the value of the function at the beginning and end of the interval:
f(6) = 6^2 - 4 = 36 - 4 = 32
f(6.25) = 6.25^2 - 4 = 39.0625 - 4 = 35.0625
Next, let's calculate the change in the function's values:
Change in f(x) = f(6.25) - f(6) = 35.0625 - 32 = 3.0625
Finally, let's calculate the change in x:
Change in x = 6.25 - 6 = 0.25
Now, we can find the average rate of change:
Average rate of change = Change in f(x) / Change in x = 3.0625 / 0.25 = 12.25