Final answer:
The average rate of change for the function 3x-6/x-2 with an interval of [6,8] is 0.
Step-by-step explanation:
To find the average rate of change for the function 3x-6/x-2 over the interval [6,8], we need to calculate the change in the function's value divided by the change in the input variable. The formula for average rate of change is (f(b) - f(a)) / (b - a), where f(x) represents the function and a and b represent the interval endpoints. In this case, we have f(x) = 3x-6/x-2, a = 6, and b = 8. Plugging these values into the formula, we get: (3(8)-6/(8)-2) - (3(6)-6/(6)-2). Simplifying the expression, we get: (24-6)/(8-2) - (18-6)/(6-2) = 18/6 - 12/4 = 3 - 3 = 0. Therefore, the average rate of change for the function over the given interval is 0.