The average rate of change of a continuous function f(x) in an interval (a, b) is
(f(b) - f(a)) / (b - a)
So for
f(x) = 3x ² + 2x + 5
on the interval (0, 2), we have
• f (2) = 3 • 2² + 2 • 2 + 5 = 21
• f (0) = = 3 • 0² + 2 • 0 + 5 = 5
so that the average rate of change is
(f (2) - f (0)) / (2 - 0) = (21 - 5) / 2 = 16 / 2 = 8
and the answer is B.
