What is the average rate of change of [0,4], [4,7], [7,9] or [9,12]
To find the average rate of change, we need to calculate the rate of change for each interval and then find the average of those rates.
The rate of change for an interval is given by the change in the dependent variable divided by the change in the independent variable.
For the interval [0,4]:
Change in dependent variable = 7 - 4 = 3
Change in independent variable = 4 - 0 = 4
Rate of change = 3/4
For the interval [4,7]:
Change in dependent variable = 9 - 7 = 2
Change in independent variable = 7 - 4 = 3
Rate of change = 2/3
For the interval [7,9]:
Change in dependent variable = 12 - 9 = 3
Change in independent variable = 9 - 7 = 2
Rate of change = 3/2
For the interval [9,12]:
Change in dependent variable = N/A (Not Applicable since there is only one value)
Change in independent variable = 12 - 9 = 3
Rate of change = N/A
To find the average rate of change, we add up the rates of change for each interval and divide by the number of intervals with defined rates:
(3/4 + 2/3 + 3/2) / 3 = (9/12 + 8/12 + 18/12) / 3 = 35/12 / 3 = 35/36 = 0.972
Therefore, the average rate of change for the intervals [0,4], [4,7], [7,9], and [9,12] is approximately 0.972.