Estimation of points of rapid change in the mean function m(t) is considered under long memory residuals, irregularily spaced time points and smoothly changing marginal distributions obtained by local Gaussian subordination. The approach is based on kernel estimation of derivatives of the trend function. An asymptotic expression for the mean squared error is obtained. Limit theorems are derived for derivatives of m and the time points where rapid change occurs. The results are illustrated by an application to measurements of oxygen isotopes trapped in the Greenland ice sheets during the last 20,000 years.