# [R] how to compute maximum of fitted polynomial?

Tue Jun 4 23:51:48 CEST 2013

```Hello,

As for the first question, you can use ?optim to compute the maximum of
a function. Note that by default optim minimizes, to maximize you must
set the parameter control\$fnscale to a negative value.

fit <- lm(y ~ poly(x, 3))

fn <- function(x, coefs) as.numeric(c(1, x, x^2, x^3) %*% coefs)

sol <- optim(0, fn, gr = NULL, coef(fit), control = list(fnscale = -1),
method = "L-BFGS-B", lower = 0, upper = 1)

As for the second question, I believe you can do something like

dfdx <- D( expression(a + b*x + c*x^2 + d*x^3), "x")

a <- coef(fit)[1]
b <- coef(fit)[2]
c <- coef(fit)[3]
d <- coef(fit)[4]
x <- sol\$par
eval(dfdx)

See the help page for ?D

Hope this helps,

Em 04-06-2013 21:32, Joseph Clark escreveu:
> My script fits a third-order polynomial to my data with something like this:
>
> model <- lm( y ~ poly(x, 3) )
>
> What I'd like to do is find the theoretical maximum of the polynomial (i.e. the x at which "model" predicts the highest y).  Specifically, I'd like to predict the maximum between 0 <= x <= 1.
>
> What's the best way to accomplish that in R?
>
> Bonus question: can R give me the derivative or 2nd derivative of the polynomial?  I'd like to be able to compute these at that maximum point.
>
> Thanks in advance!
>
>
> // joseph w. clark , phd , visiting research associate
> \\ university of nebraska at omaha - college of IS&T
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>

```