Answer: 7
Step-by-step explanation: The average rate of change of a function f(x) over an interval [a,b] is defined as the ratio of “change in the function values” to the "change in the endpoints of the interval"1. In other words, it is the slope of the line that passes through two points on the graph of f(x)2.
To find the average rate of change of f(x) = x² + x + 4 from x = 2 to x = 4, we can use this formula:
Average rate of change = [f(4) - f(2)] / (4 - 2)
First, we need to plug in x = 4 and x = 2 into f(x) and simplify:
f(4) = (4)² + (4) + 4 f(4) = 16 + 8 f(4) = 24
f(2) = (2)² + (2) + 4 f(2) = 4 + 6 f(2) = 10
Next, we need to subtract f(2) from f(4), and divide by (4 - 2):
Average rate of change = [24 - 10] / (4 - 2) Average rate of change = 14 / 2 Average rate of change = 7