If f (x) = x^2+3x, what is the average rate of change of f (x) over the interval [-2,3]?

the average rate of change in the closed interval [ a, b ] is

(f (b) - f (a))) / (b - a)

f (b) = f (3) = 3² + 3 (3) = 9 + 9 = 18

f (a) = f (-2) = (-2) ² + 3 (-2) = 4 - 6 = - 2

= (18 - (-2)) / (3 - (-2)) = 20/5 = 4