tangent | R Documentation |

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

```
tangent(p, x0)
```

`p` |
A polynomial object |

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

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

```
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)
```

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