To find the average rate of change of the function $f(x) = x^3$ between $x = 0.6$ and $x = 3.5$, use the formula:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

where $a = 0.6$ and $b = 3.5$.

1. Calculate $f(0.6)$: $f(0.6) = (0.6)^3 = 0.216$

2. Calculate $f(3.5)$: $f(3.5) = (3.5)^3 = 42.875$

3. Apply the average rate of change formula: $\text{Average Rate of Change} = \frac{42.875 - 0.216}{3.5 - 0.6} = \frac{42.659}{2.9} \approx 14.710$

Rounding to the nearest tenth:

$\text{Average Rate of Change} \approx \boxed{14.7}$

Would you like more details or have any questions?

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Here are some related questions:

1. How does the average rate of change for $f(x) = x^3$ compare to that of a linear function?
2. What is the significance of the interval length in the calculation of the average rate of change?
3. How would the average rate of change differ for $f(x) = x^2$ over the same interval?
4. Can you estimate the instantaneous rate of change at $x = 2.05$ for $f(x) = x^3$?
5. What is the geometric interpretation of the average rate of change for a cubic function?
6. How does changing the interval affect the average rate of change?
7. How would you calculate the average rate of change for a function like $f(x) = \sin(x)$ over a given interval?
8. How is the average rate of change used in real-world applications, such as physics or economics?

Tip: When calculating average rates of change, pay close attention to rounding instructions as they can affect the precision of your final answer.