Recall that the average rate of change of a function in a given interval [a, b] is given by:
(f(b) - f(a)) / (b-a)
so for the function: f(x) = x^2 + 3 x
in the interval [4 , 7] is going to be:
[ f(7) - f(4) ] / (7-4) = [70 - 28] / 3 = 42 / 3 = 14
Then the average rate of change is: 14