This is problem #83 on the 1998 AP Calculus test. How is this solved?

The Taylor series for ln(x), centered at x=1, is sigma((-1)^(n+1) * (x-1)^n/n) for n goes from 1 to infinity. Let f be the function given by the sum of the first three nonzero terms of this series.

Find the maximum value of abs(lnx - f(x)).

(The answer is given to be 0.145)