We present a Bayesian scheme for estimation of the location of an extremum of the first or second derivative of a noisy signal in a given interval using a scale-recursive multiresolution approach, as a means to locate edges or transition points. The estimation is carried out on the wavelet coefficients using a coarse-To-fine cross-scale search. A prior is specified for the location of the extremum at a given scale based on a location estimate at a coarser scale and a likelihood function is specified based on a rank-ordered version of the wavelet coefficients, leading to a MAP estimate at the given scale. This then becomes the location parameter for the prior at the next finer scale in a scale-recursive MAP estimation scheme. We include examples using both synthetic signals and optically measured cardiac electrical signals.