the average rate of change of f(x)=4x^2+6 over the interval 6< x < 12 is
The average rate of change of a function over an interval is calculated by taking the difference in the function values at the endpoints of the interval and dividing by the difference in the input values:
f(12) - f(6) / 12 - 6
f(12) = 4(12)^2 + 6 = 576 + 6 = 582
f(6) = 4(6)^2 + 6 = 144 + 6 = 150
Therefore, the average rate of change over the interval 6 < x < 12 is:
(582 - 150) / (12 - 6) = 432 / 6 = 72