To find the average rate of change of a 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 \( b = 4 \).
You need the values of \( f(1) \) and \( f(4) \) to compute this. Assuming you have those values or you’ve calculated it and the results yield one of the options given, you can choose accordingly.
Since I don’t have the specific function or its output at those points, I can't calculate the exact average rate of change. However, if you apply the above formula to your function and determine the values of \( f(1) \) and \( f(4) \), you can select one of the following responses as appropriate based on your calculations:
- The average rate of change is −13.
- The average rate of change is negative \( \frac{1}{2} \).
- The average rate of change is 3.
- The average rate of change is 1.
- The average rate of change is 13.
Please calculate the average rate of change using the function's values for \( f(1) \) and \( f(4) \), and select the correct response from the options provided.