Question

What is the average rate of change in f(x) over the interval [1,5]?

a) -6
b) -1/2
c) 1/4
d) 1

Answer 1

The average rate of change in f(x) over the interval [1,5] can be found by calculating the difference between the values of f(x) at the endpoints of the interval and then dividing by the difference in input values. The correct answer is b) -1/2.

Step-by-step explanation:

The average rate of change in f(x) over the interval [1,5] can be found by calculating the difference between the values of f(x) at the endpoints of the interval and then dividing by the difference in input values.

Let's denote f(1) as y1 and f(5) as y2. Then the average rate of change is given by:

Average rate of change = (y2 - y1) / (5 - 1)

By subtracting the function values and dividing by the interval length, we get the average rate of change.

Therefore, the correct answer is b) -1/2.