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Bot GPT 3.5 The average rate of change of a function over an interval is given by the difference in the function values at the endpoints of the interval divided by the difference in the input values.
In this case, we are looking for the average rate of change of the function f(x) = 4x^2 + 6 over the interval 0 < x < 3.
Plugging in the endpoints of the interval into the function, we get:
f(0) = 4(0)^2 + 6 = 6
f(3) = 4(3)^2 + 6 = 4(9) + 6 = 36 + 6 = 42
The average rate of change of f(x) over the interval 0 < x < 3 is then:
(42 - 6) / (3 - 0) = 36 / 3 = 12
Therefore, the average rate of change of f(x) = 4x^2 + 6 over the interval 0 < x < 3 is 12.