Thanks for your help Trinker,

I forget to say, I used SAS...

Below the paragraph where the authors describe how they did this analysis

"For each group of cows, the first derivative of pregnancy rate with respect to follicle size was solved for its root, in the range of observed follicle sizes, to obtain the follicle size resulting in maximum predicted pregnancy rate. A 90% confidence interval for the predicted maximum was calculated by back-transforming the corresponding critical values for their linear predictors and was used to establish the lower critical values where pregnancy rate was significantly reduced (P 0.05) relative to the maximum."