If you are using piecewise quadratic polynomials to approximate the function $f (x) = \ln x$ on the interval $[1, 2]$

Question

If you are using piecewise quadratic polynomials to approximate the function $f (x) = \ln x$ on the interval $[1, 2]$ and expect the maximum error to be smaller than $10^{-6}$, how many subintervals do you need?