Final answer:
The average rate of change of the function f(x) = x² - 4 from x = 5 to x = 2 is calculated by finding the values of f(x) at those points and then dividing the difference in function values by the difference in x values. The result comes out to be 7, so option D is correct.
Step-by-step explanation:
The question asks us to calculate the average rate of change of the function f(x) = x² - 4 from x = 5 to x = 2. The average rate of change is defined as the change in the function's value divided by the change in x, which is similar to the slope of the secant line between the two points on the graph of the function.
To calculate it, we first find the values of f(x) at x = 5 and x = 2:
- f(5) = 5² - 4 = 25 - 4 = 21
- f(2) = 2² - 4 = 4 - 4 = 0
Now, we use the values to find the average rate of change:
Average rate of change = (f(5) - f(2)) / (5 - 2) = (21 - 0) / (3) = 21 / 3 = 7
Thus, the average rate of change of f(x) from 5 to 2 is 7. The correct option is D. 7.