Final answer:
To find the average rate of change of f(x) on the interval [2, 2+h], we need to calculate f(2) and f(2+h) and then use the formula (f(2+h) - f(2))/h. After substituting the values, we find the average rate of change to be 8 + 2h.
Step-by-step explanation:
To find the average rate of change of f(x) on the interval [2, 2+h], we need to first find the values of f(x) at x = 2 and x = 2+h.
For x = 2:
f(2) = 2(2)^2 + 3 = 11
For x = 2+h:
f(2+h) = 2(2+h)^2 + 3 = 2(4+4h+h^2) + 3 = 8 + 8h + 2h^2 + 3 = 11 + 8h + 2h^2
The average rate of change is given by the formula (f(2+h) - f(2))/h. Substituting the values we found above:
Average rate of change = (11 + 8h + 2h^2 - 11)/h = (8h + 2h^2)/h = 8 + 2h