  The multiplier $\lambda_n$ of a periodic orbit of period $n$ can be viewed as
a (multiple-valued) algebraic function on the space of all complex quadratic
polynomials $p_c(z)=z^2+c$. We provide a numerical algorithm for computing
critical points of this function (i.e., points where the derivative of the
multiplier with respect to the complex parameter $c$ vanishes). We use this
algorithm to compute critical points of $\lambda_n$ up to period $n=10$.
