Final answer:
To find the average rate of change of a function over an interval, evaluate the function at the endpoints of the interval and divide the difference in the function values by the difference in the input values. In this case, the average rate of change is -5.
Step-by-step explanation:
The average rate of change of a function over an interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing that by the difference in the input values. In this case, the interval is from x=3 to x=4. So, the average rate of change of the function over this interval can be found by:
average rate of change = (f(4) - f(3))/(4 - 3)
Substitute the provided function values and evaluate to find the average rate of change.
average rate of change = (4(4) - 7(3))/(4 - 3)
average rate of change = (16 - 21)/(4 - 3)
average rate of change = -5/1
Therefore, the average rate of change of the function over the interval from x=3 to x=4 is -5.