I need to find the root of the second derivative of many curves and do not
want
to cut and paste the expression results from the deriv() or D() functions
every time. Below is an
example. What I need to do is refer to "fn2nd" in the uniroot() function,
but when I
try something like uniroot(fn2nd,c(0,1)) I get an error, so I have resorted
to pasting
in the expression, but this is highly inefficient.
Thanks, J
y <- c(9.9,10,10,9.5,9,6,3,1,0,0,0)
b <- seq(0,1,by=0.1)
dat <- data.frame(y = y, b = b)
plot(y ~ b, xlim = c(0,1), ylim= c(-12,12))
fn <- nls(y ~ asym/(1 + exp(p * b - q)),data = dat, list(asym=10,p=16,q=7),
trace=T)
curve(10.001/(1 + exp(14.094 * x - 7.551)), from = 0, to = 1, add = T)
fn2 <- expression(10.001/(1 + exp(14.094 * x - 7.551)))
fn2nd <- D(D(fn2, "x"), "x")
ex <- seq.int(from=0, to=1, length.out = 1000)
y1 <- eval(fn2nd, envir = list(x = ex), enclos = parent.frame())
lines(ex, y1, type = "l")
r <- uniroot(function(x) -(10.001 * (exp(14.094 * x - 7.551) * 14.094 *
14.094)/(1 + exp(14.094 *
x - 7.551))^2 - 10.001 * (exp(14.094 * x - 7.551) * 14.094) *
(2 * (exp(14.094 * x - 7.551) * 14.094 * (1 + exp(14.094 *
x - 7.551))))/((1 + exp(14.094 * x -
7.551))^2)^2),interval=c(0,1),tol = 0.0001)
r$root
abline(h=0, col = "red")
abline(v=r$root, col = "green")
arrows(0.6, -2, r$root,0, length = 0.1, angle = 30, code = 2, col = "red")
text(0.765,-2.3,paste("b = ",r$root,sep=""))
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