Final answer:
The average rate of change for the function over the given interval is approximately 1.9, rounded to the nearest tenth.
Step-by-step explanation:
The question asks to find the average rate of change of the function f(x) = 14√x - 12 over the interval [10, 17]. To find the average rate of change, we use the formula:
Average rate of change = ∑(f(b) - f(a)) / (b - a)
Apply the function to points 10 and 17:
- f(10) = 14√10 - 12
- f(17) = 14√17 - 12
Calculate the values:
- f(10) = 14 * 3.1623 - 12 ≈ 32.2714
- f(17) = 14 * 4.1231 - 12 ≈ 45.7234
Now calculate the average rate of change:
∑(f(17) - f(10)) / (17 - 10) = (45.7234 - 32.2714) / 7 = 13.452 / 7 ≈ 1.922
Rounded to the nearest tenth, the average rate of change is 1.9.