Final answer:
The average rate of change over the interval [-2,3] for the function f(x) = 3x + 4 is 4.2.
Step-by-step explanation:
The average rate of change for a function is calculated by finding the difference in the function's values over the interval and dividing by the difference in the input values. In this case, we have the function f(x) = 3x + 4 and the interval is [-2, 3].
To find the average rate of change, we plug in the endpoints of the interval into the function and calculate the difference:
f(3) - f(-2) = (3(3) + 4) - (3(-2) + 4) = 19 - (-2) = 21
Next, we find the difference in the input values:
3 - (-2) = 5
Finally, we divide the difference in the function values by the difference in the input values:
Average rate of change = 21 / 5 = 4.2