I have used the second order Taylor polynomial for the square root of x about x=100 to approximate the square root of 101, to which I got 80,399/8,000 = 10.049875. Then I calculated the error and got 1/1,600,000 = 0.000,000,625. Neither of those were any problem.
However, how can I know if the answer I got from using Taylor is actually higher or lower than the actual value of the square root of 101?
When I use the calculator I get the answer 10.04987562, so I know my answer from using Taylor is too low, but how can I know?
I have to explain why it is either higher or lower without using a calculator.
Also, if someone wants to fix my post to make it look better, that's fine, I haven't quite figured out to write math stuff on a computer yet.. Thanks :)