Final answer:
The average rate of change of the function f(x) = x^3 - 2x + 1 over the interval [-3, -2] is calculated using the formula for average rate of change and is found to be 17.
Step-by-step explanation:
The question asks to find the average rate of change of the function f(x) = x^3 - 2x + 1 over the interval [-3, -2]. To do this, we can apply the formula for average rate of change:
\[\frac{f(b) - f(a)}{b - a}\]
Plugging in the given endpoints of the interval, we get:
\[\frac{f(-2) - f(-3)}{-2 - (-3)} = \frac{((-2)^3 - 2(-2) + 1) - ((-3)^3 - 2(-3) + 1)}{-2 + 3}\]
\[= \frac{(-8 + 4 + 1) - (-27 + 6 + 1)}{1}\]
\[= \frac{(-3) - (-20)}{1}\]
\[= \frac{17}{1}\]
\[= 17\]
Therefore, the average rate of change of the function over the given interval is 17.