To find the average rate of change of the function f(x) = 17x² over the interval [1, 5], we use the formula for average rate of change, which is:
Average rate of change = (f(b) – f(a)) / (b – a)
In this case, a = 1 and b = 5. We will start by calculating f(1) and f(5):
- f(1) = 17(1)² = 17
- f(5) = 17(5)² = 17(25) = 425
Now, we can substitute these values into the average rate of change formula:
Average rate of change = (f(5) – f(1)) / (5 – 1)
Substituting in our values:
Average rate of change = (425 – 17) / (5 – 1)
Average rate of change = 408 / 4
Average rate of change = 102
Thus, the average rate of change of f(x) = 17x² over the interval [1, 5] is 102.