
Error Bounds
Sorry if this isn't the right place for this, I thought it was closest but I might be wrong.
So we are estimated derivatives using a three point formula in class and the giving bounds for the error. I was given a table of x1=1.1, x2=1.2, x3=1.3, x4=1.4. I have to find an error bound to estimate the error for x=1.1 and 1.3 for f(x)=e^{x}
In class we did x=1.1 as follows
error<=(h^{2}/_{3})e^{g(x)} for some g between (1.1, 1.3)
error<=(h^{2}/_{3})e^{1.3 }I understand all of this, except why it is between 1.1 and 1.3. I went to do the x3 error bound, and I wasn't sure what to choose for my upper bound. She added 2h to it, so would I use 1.5, even though it's not in my table?