Final answer:
The average rate of change of the function f(x) = 2x² - 2 from x = 2 to x = 6 is calculated as the change in function values over the change in x, which is 16.
Step-by-step explanation:
To find the average rate of change of the function f(x) = 2x² - 2 from x = 2 to x = 6, we need to calculate the difference in the function's values at these points and divide by the interval over which the change occurs. This is similar to finding the slope of the secant line that connects the points (2, f(2)) and (6, f(6)) on the graph of the function.
First, we evaluate the function at both points:
- f(2) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6
- f(6) = 2(6)² - 2 = 2(36) - 2 = 72 - 2 = 70
Now, we use these values to find the average rate of change:
Average rate of change = ∆f /∆x = (f(6) - f(2)) / (6 - 2) = (70 - 6) / (4) = 64 / 4 = 16
So, the average rate of change of f(x) from 2 to 6 is 16.