Final answer:
To find the average rate of change for the function f(x) over the interval from x = 7 to x = 12, calculate the values of the function at x = 7 and x = 12, subtract the former from the latter, and divide by the difference in x values, which is 5.
Step-by-step explanation:
The student has asked to find the average rate of change of the function f(x) = 1.1x³ - 35x² + 264x + 557 over the interval from x¹ = 7 to x² = 12. The average rate of change is calculated using the formula:
\(\frac{f(x²) - f(x¹)}{x² - x¹}\)
First, we evaluate the function at the two points:
- f(7) = 1.1(7)³ - 35(7)² + 264(7) + 557
- f(12) = 1.1(12)³ - 35(12)² + 264(12) + 557
After calculating the values of f(7) and f(12), we subtract the former from the latter and divide by the difference in x values, x² - x¹ = 12 - 7 = 5, to get the average rate of change.
Example Calculation:
- Calculate f(7) and f(12).
- Subtract f(7) from f(12).
- Divide the result by 5 (the difference between 12 and 7).
The result is the average rate of change of the function over the interval from x = 7 to x = 12.