00:01
Okay, so we are given the function f of t equals the square root of 9t, and we're given the intervals t equals 6 to 6 plus h.
00:11
We are going to find the average rate of change.
00:14
To do this, average rate of change, we are going to determine the value of the function at 6 plus h, and then the value of the function at 6, and then divide it out by the bounds, subtract it from each other.
00:32
So what we get here is the square root of 9 times t plus h, minus the square root of 54, so h times h is 54, all divided by h.
00:47
To figure this out, what we're going to first do is we're just going to take the, multiply each side by the conjugate here, in order to cancel it out and get something a little nicer.
00:58
And to do that, we're just going to write exactly the same thing that we have in the numerator, but we're going to switch the sign to the middle, and then we're going to do that on the top and bottom, so we're not changing the overall value of this function...