Question

Use the average rate of change to describe the graph of f(x) over the interval [1,4].
A) The average rate of change is −1/3.
B) The average rate of change is 1/3.
C) The average rate of change is 3.
D) The average rate of change is 1

Answer 1

To determine the average rate of change of the function \( f(x) \) over the interval \([1, 4]\), you can use the formula:

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

where \( a = 1 \) and \( b = 4 \).

1. **Evaluate \( f(1) \) and \( f(4) \)**: Without the specific function \( f(x) \), I can't calculate these values directly. However, if you provide the function or its values at \( x = 1 \) and \( x = 4 \), I can proceed with the calculation.

2. **Substitute into the formula**: Once you have the values for \( f(1) \) and \( f(4) \), substitute them into the formula to find the average rate of change.

3. **Choose the correct option**: Compare the computed average rate of change to the options provided to find the correct answer.

If you can provide the function \( f(x) \) or its values at the points \( x = 1 \) and \( x = 4 \), I can help you calculate it.