how to compute maximum of fitted polynomial?

David Winsemius <dwinsemius <at> comcast.net> writes:

[...]

On Jun 4, 2013, at 10:15 PM, Hans W Borchers wrote:

In the case of polynomials, "elementary math ... methods" can  
actually be
executed with R:

library(polynomial)                 # -6 + 11*x - 6*x^2 + x^3
    p0 <- polynomial(c(-6, 11, -6, 1))  # has zeros at 1, 2, and 3
    p1 <- deriv(p0); p2 <- deriv(p1)    # first and second derivative
    xm <- solve(p1)                     # maxima and minima of p0
    xmax = xm[predict(p2, xm) < 0]      # select the maxima
    xmax                                # [1] 1.42265

These look like the functions present in the 'polynom' package  
authored by Bill Venables [aut] (S original), Kurt Hornik [aut, cre]  
(R port), Martin Maechler. I wasn't able to find a 'polynomial'  
package on CRAN. The 'mpoly' package by David Kahle offers  
multivariate symbolic operations as well.

Sorry, yes of course, it should be `library(polynom)`.
Somehow I'm making this mistake again and again.
And one has to be a bit careful about complex roots.


Hans Werner