R help - Jan 2012 - find inflexion point of discrete value list with R

i have a list of values like this

x y
1 3
2 2
3 3
4 4
5 5
6 4
7 3
8 2
9 3

and need the inflexion points (and all max and min).
Is there a nice way to get the local max, min and inflexion points?

kind regards,

-- 
Jonas Stein <news at jonasstein.de>

Jonas Stein <news <at> jonasstein.de> writes:
> 
> i have a list of values like this
> 
> x y
> 1 3
> 2 2
  [snip]
> 
> and need the inflexion points (and all max and min).
> Is there a nice way to get the local max, min and inflexion points?
  diff(y) gives you the first difference, the analogue of the gradient
  diff(diff(y)) gives the second difference, the analogue of the second
derivative.

  dy <- diff(y)
  d2y <- diff(dy)
  which(dy==0)  ## critical values
  sign(s2y)[which(dy==0)]  ## test for max/min/saddle
  which(d2y==0)   ## inflection points

Ben Bolker <bbolker <at> gmail.com> writes:
> 
> Jonas Stein <news <at> jonasstein.de> writes:
>   [snip]
> 
  [snip]
>   sign(s2y)[which(dy==0)]  ## test for max/min/saddle
  oops, obviously this should be sign(d2y)[which(dy==0)]