For this case what we should do is evaluate the function in each of the points from 2 to 7 and then find the average. We have then: f (x) = ln (3x) +2.5. f (2) = ln (3 * 2) + 2.5 = 4.291759469 f (3) = ln (3 * 3) + 2.5 = 4.697224577 f (4) = ln (3 * 4) + 2.5 = 4.98490665 f (5) = ln (3 * 5) + 2.5 = 5.208050201 f (6) = ln (3 * 6) + 2.5 = 5.390371758 f (7) = ln (3 * 7) + 2.5 = 5.544522438 Then the average is: Average = (4.291759469 + 4.697224577 + 4.98490665 + 5.208050201 + 5.390371758 + 5.544522438) / (6) = 5.019472516 nearest hundredth 5.02 Answer: the average rate of change of f (x) from 2 to 7 is 5.02
