R: Tangent lines

tangent {PolynomF} | R Documentation

## Tangent lines

### Description

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

### Usage

    tangent(p, x0)

### Arguments

`p` | A polynomial object
`x0` | A numeric vector of values at which the tangent line(s) are required

### Value

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

### 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)

[Package PolynomF version 2.0-5 Index]