00:01
Hi there, we are given the function fx which is equal to log x and we want to find the value of f x up to two decimal places for x equal to 1, x equal to 1 .5, x equal to 2, x equal to 2 .5 and x equal to 3.
00:18
Now, log of 1 is 0, log of 1 .5 is 0 .18, log of 2 is 0 .30, log of 2 .5 is 0 .40, log of 2 .5 is 0 .40, and log of 3 is 0 .48.
00:42
Next, we want to find the average rate of change of fx between x equal to 1 and x equal to 3, which is given by delta f x divided by delta x which is equal to f of 3 minus f of 1 divided by 3 minus 1 which is now since f of 3 is 0 .48 minus f of 1 which is 0 divided by 3 minus 1 which is 2 so this is equal to 0 .24.
01:20
Therefore, rate of change between x equal to 1 and x equal to 3 is 0 .24.
01:39
Next, we want to find the instantaneous rate of change of fx at x equal to 2...