If the average rate of change of g(x) from x = 1 to x = 9 is 20, and if the average rate of change of g(x) from x = 9 to x = 21 is 40, then what is the average rate of change of g(x) from x = 1 to x = 21?
from 1 to 9, g(x) = 20(x-1)
so, g(9) = g(1) + 160
similarly, g(21) = g(9) + 40(21-9)
= g(9) + 480
So, g(21) = g(1) + 160 + 480 = g(1)+640
640/(21-1) = 640/20 = 32
The average rate of change from x=1 to 21 is 32.
solve using the graphing method y=x-3
y=-1/2x=3
To find the average rate of change of g(x) from x = 1 to x = 21, we first need to determine the change in g(x) over that interval. We can then calculate the average rate of change by dividing the change in g(x) by the change in x.
The change in g(x) from x = 1 to x = 21 can be found by adding the changes in g(x) from 1 to 9 and from 9 to 21. The given information tells us that the average rate of change from x = 1 to x = 9 is 20, meaning that g(x) increases by an average of 20 units per unit increase in x. So, the change in g(x) from x = 1 to x = 9 is (9 - 1) * 20 = 8 * 20 = 160.
Similarly, the given information tells us that the average rate of change from x = 9 to x = 21 is 40, meaning that g(x) increases by an average of 40 units per unit increase in x. Therefore, the change in g(x) from x = 9 to x = 21 is (21 - 9) * 40 = 12 * 40 = 480.
To find the average rate of change from x = 1 to x = 21, we need to divide the change in g(x) (which is the sum of the changes from x = 1 to x = 9 and from x = 9 to x = 21) by the change in x (which is 21 - 1 = 20). Therefore, the average rate of change of g(x) from x = 1 to x = 21 is (160 + 480)/20 = 640/20 = 32.
So, the average rate of change of g(x) from x = 1 to x = 21 is 32 units per unit increase in x.