Final answer:
The average rate of change of the function F(x) = x² - 9x + 16 over the interval from x = -1 to x = 9 is -1.
Step-by-step explanation:
The average rate of change of the function F(x) = x² - 9x + 16 over the interval -1≤x≤9 is found by taking the difference in the function values at the endpoints of the interval, divided by the difference in x values. To calculate this, we evaluate F(9) and F(-1), and then use the formula: average rate of change = (F(9) - F(-1))/(9 - (-1)).
Calculating F(9) gives us 9² - 9· 9 + 16 = 81 - 81 + 16 = 16. Calculating F(-1) gives us (-1)² - 9·(-1) + 16 = 1 + 9 + 16 = 26. Now we find the average rate of change: (16 - 26)/(9 - (-1)) = (-10)/(10) = -1.
The average rate of change of the function over the given interval is -1.