Compute the average rate of change of f(x) = 9x 2 + 2 from x 1 = 4 to x 2 = 7. Round your answer to two decimal places.

To compute the average rate of change of a function, we need to find the difference in the function values divided by the difference in the input values. In this case, we need to find the average rate of change of f(x) = 9x^2 + 2 from x1 = 4 to x2 = 7.

First, let's find the value of f(x) at x1 and x2.
f(x1) = 9(4)^2 + 2 = 9(16) + 2 = 144 + 2 = 146
f(x2) = 9(7)^2 + 2 = 9(49) + 2 = 441 + 2 = 443

Now, we can find the difference in function values:
Difference in function values = f(x2) - f(x1) = 443 - 146 = 297

Next, let's find the difference in the input values:
Difference in input values = x2 - x1 = 7 - 4 = 3

Finally, we can calculate the average rate of change:
Average rate of change = Difference in function values / Difference in input values = 297 / 3 = 99

Therefore, the average rate of change of f(x) = 9x^2 + 2 from x1 = 4 to x2 = 7 is 99 (rounded to two decimal places).