PolynomF (version 2.0-8)

tangent: Tangent lines

Description

Find the tangent line to a polynomial at one or more x-points

Usage

tangent(p, x0)

Value

A linear polynomial giving the tangent line, or a list of such polynomials

Arguments

p

A polynomial object

x0

A numeric vector of values at which the tangent line(s) are required

Examples

p <- poly_from_zeros(c(0, 0:5, 4))
plot(p, xlab = expression(italic(x)), ylab = expression(italic(P(x))),
  main = parse(text = paste("italic(P(x) ==",
                             as.character(p, decreasing = TRUE),")")))
x0 <- solve(deriv(p))        ## stationary points
lines(tangent(p, x0), col = "dark green", lty = "solid",
      limits = cbind(x0-1/4, x0+1/4))
points(x0, p(x0), col = "dark green")

x0 <- solve(deriv(deriv(p))) ## points of inflexion
lines(tangent(p, x0), col = "red", lty = "solid", lwd = 2,
      limits = cbind(x0-1/4, x0+1/4))
points(x0, p(x0), col = "red")
legend("bottomleft", c("Stationary points", "Points of inflexion"),
       pch = 19, col = c("dark green", "red"), lty = "solid",
       cex = 0.7, bg = "beige", box.lwd = 0.25)