Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 40, is less than or equal to, x, is less than or equal to, 40≤x≤55.
xx f, of, xf(x)
10 29
25 23
40 17
55 11
70 5
85 −1
The average rate of change over the interval between x = 40 and x = 55 is calculated by finding the difference in the function values at the endpoints of the interval and then dividing by the difference in the x-values.
First, find f(55) and f(40):
f(55) = 11
f(40) = 17
Next, calculate the average rate of change:
Average rate of change = (f(55) - f(40))/(55 - 40)
Average rate of change = (11 - 17)/(55 - 40)
Average rate of change = -6/15
Average rate of change = -2/5
Therefore, the average rate of change of the function over the interval 40≤x≤55 is -2/5.