[R] Inflection point on a curve

[FMH]

Dear All,

I have been trying to find an inflection point from a nonparametric model, for instance on  a series of Economics, Financial, Environmental data, which was fitted via sm.regression package, but have difficulty to find the derivative of the model. The following are the data and the codes to fit such a nonparametric model.

#######################################################
library(sm)
x <- c(6.3,  6.6,  7.0,  8.0,  8.8,  9.8, 12.0, 14.2, 15.5, 15.7, 15.8) 
y <- rev(seq(1,51,by=5))
sm.regression(x,y,method = "cv", col = "red")
#######################################################


Could someone please advice me an appropriate way to determine such an inflection point from the nonparametric model?

Thank you
Fir