Question

Use the average rate of change to describe the graph of f (x) over the interval [1, 4]

Answer 1

To describe the graph of the function \( f(x) \) over the interval \([1, 4]\) using the average rate of change, we first need to determine the average rate of change of the function over that interval.

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is calculated using the formula:

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

In your case, \( a = 1 \) and \( b = 4 \). You'll need to evaluate the function \( f \) at these two points:

1. Calculate \( f(1) \).
2. Calculate \( f(4) \).

Substituting these values into the formula will give you the average rate of change over the interval \([1, 4]\).

Once you've calculated the average rate of change, you can interpret the result:

- If the average rate of change is positive, it indicates that the function \( f(x) \) is increasing on the interval.
- If it is negative, then \( f(x) \) is decreasing.
- If it is zero, then the function is constant over that interval.

If you provide the specific function \( f(x) \), I can help you calculate the average rate of change and provide a more detailed description of the graph.