Análisis Visual del Método de Newton-Raphson

0.1 aa

#ejemplo
f <- function(x){x ** 2-3}
fprima <- function(x){2*x}

0.2 1

curve(f,0,4,lwd=2,col='red')
abline(h=0,v=0)

x0 <- 1
curve(x*fprima(x0)+(f(x0)-x0*fprima(x0)),lwd=1,col=2,add=T)
segments(x0,f(x0),x0,0)
points(x0,0,pch=16,col='magenta')
points(x0,f(x0),pch=16,col='blue')


x0 <- 1
curve(x*fprima(x0)+(f(x0)-x0*fprima(x0)),lwd=1,col=2,add=T)
segments(x0,f(x0),x0,0)
points(x0,0,pch=16,col='magenta')
points(x0,f(x0),pch=16,col='blue')


x0 <- x0 - f(x0)/fprima(x0)
curve(x*fprima(x0)+(f(x0)-x0*fprima(x0)),lwd=2,col=sample(1:7,1) ,add=T)

segments(x0,f(x0),x0,0)
points(x0,0,pch=16)
points(x0,f(x0),pch=16,col='blue')


x0 <- x0 - f(x0)/fprima(x0)
curve(x*fprima(x0)+(f(x0)-x0*fprima(x0)),lwd=2,col=sample(1:7,1) ,add=T)

segments(x0,f(x0),x0,0)
points(x0,0,pch=16)
points(x0,f(x0),pch=16,col='green')

x0

## [1] 1.75

0.3 Solución

sqrt(3)

## [1] 1.732051

f(x0)

## [1] 0.0625