Final answer:
The average rate of change of the function f(x) = 1/(x+11) on the interval (6, 6 + h) is calculated using the difference quotient. It results in the expression [1/(17 + h) - 1/17] / h.
Step-by-step explanation:
To find the average rate of change of the function f(x) = 1/(x+11) on the interval (6, 6 + h), we need to use the average rate of change formula:
Average rate of change = ∆f/∆x = [f(x2) - f(x1)] / [x2 - x1]
Let x1 = 6 and x2 = 6 + h. Therefore:
f(x1) = f(6) = 1/(6 + 11) = 1/17
f(x2) = f(6 + h) = 1/((6 + h) + 11) = 1/(17 + h)
Now, we can substitute these values into the formula:
Average rate of change = [1/(17 + h) - 1/17] / [6 + h - 6]
Average rate of change = [1/(17 + h) - 1/17] / h
This gives us the expression for the average rate of change of f(x) on the interval (6, 6 + h).