Question

Calculate the average rate of change of f (x) = 3x2 + 2x + 5 on the interval (0, 2).
A. -1
B. 8
C. 38
D. 128

Answer 1

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.