The average rate of change of a function g(x) between two points is given by the formula:
Average Rate of Change = (g(7) – g(4)) / (7 – 4)
According to the information provided, this average rate of change equals 5/6. Therefore, we can write:
(g(7) – g(4)) / 3 = 5/6
Multiplying both sides by 3 gives:
g(7) – g(4) = (5/6) * 3 = 25/6
This tells us that:
g(7) = g(4) + 25/6
From this, we can conclude that if the average rate of change of g(x) from x = 4 to x = 7 is 5/6, then it’s true that g(7) is greater than g(4) by 25/6 units. Therefore, one must conclude that g(7) > g(4).