Question

Given the function defined in the table below,

find the average rate of change, in simplest form,
of the function over the interval 0 < x < 60.

x f(x)
0 41
15 35
30 29
45 23
60 17

Answer 1

The average rate of change of the function over the interval 0 < x < 60 is calculated as -0.4, found by using the function's starting and ending values within the interval and dividing by the interval length.

Step-by-step explanation:

To find the average rate of change of the function over the interval 0 < x < 60, we need to calculate the difference in the function's values at the endpoints of the interval and then divide by the length of the interval. The function values at x = 0 and x = 60 are 41 and 17, respectively.

The formula for the average rate of change is:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

So in this case, it would be:

Average Rate of Change = (f(60) - f(0)) / (60 - 0)

Average Rate of Change = (17 - 41) / 60

Average Rate of Change = -24 / 60

The average rate of change of the function over the interval 0 < x < 60 is -0.4.