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

Answer 1

The average rate of change of the function over the interval 0 < x < 60 is calculated by taking the difference in the function values at x = 60 and x = 0, and dividing by 60. The result is -0.4.

Step-by-step explanation:

The student is asking to find the average rate of change of a function that is defined in a table over the interval 0 < x < 60. The average rate of change of a function over an interval [a,b] is found by subtracting the function values at the endpoints and dividing by the difference in the x-values. That is, the average rate of change = (f(b) - f(a)) / (b - a).

To find this rate for the interval from x = 0 to x = 60, we will use the function values given in the table: f(60) = 17 and f(0) = 41.

So the average rate of change over the interval 0 < x < 60 is:

(f(60) - f(0)) / (60 - 0) = (17 - 41) / (60 - 0)

= -24 / 60

= -0.4