To solve the problem of calculating the average rate of change for the given function over the interval $[0, 3]$, we can use the formula:

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

where $a$ and $b$ are the endpoints of the interval.

For this problem:

• $a = 0$ and $b = 3$,
• $f(0) = 4$ and $f(3) = 14$.

Now, applying these values to the formula:

$\text{Average Rate of Change} = \frac{f(3) - f(0)}{3 - 0} = \frac{14 - 4}{3} = \frac{10}{3} \approx 3.33$

Thus, the average rate of change over the interval $[0, 3]$ is approximately 3.33.

Would you like further details or explanations on this? Here are some related questions:

1. How is the average rate of change different from instantaneous rate of change?
2. Can the average rate of change be interpreted as a slope in this context?
3. How do you calculate the rate of change for non-linear functions?
4. What happens if the interval is negative or includes negative values of $x$?
5. How does this concept apply to velocity in physics?

Tip: When calculating average rates of change, think of it as the slope of the secant line between two points on a graph.