CODEWITHSUNDEEP
rintersection
Xavier
Xavier

Reputation: 323

R - How to find the Intersection fo 2 Functions

I have 2 functions and I would like to find the values at which their intersect and plot it on the graph. How can I best achieve this? Does anyone know an R function for that?

# First Function
  func6 <- function(x)
    {
    x * log(x) - sqrt(x)
  }

  # Second Function
  func7 <- function(x)
    {
    x
  }

  x <- seq(0,10,length=100)
  plot(x, func6(x), col="blue", lwd="1", main="Graph #1")
  lines(x, func7(x), col="red")

Upvotes: 1

Views: 5757

Answers (1)

user20650
user20650

Reputation: 25854

You can use uniroot to search for the intersection; this equates to searching for the zero of the difference of the functions.

rt <- uniroot(function(x)  func6(x) - func7(x)  , c(.01,10), tol=1e-8)     
# or explicitly
# rt <- uniroot(function(x)  x * log(x) - sqrt(x) - x , c(.01,10), tol=1e-8)  

# check
all.equal(func6(rt$root), func7(rt$root))  
# [1] TRUE

Then plot it

x <- seq(0, 10, length=100)
plot(x, func6(x), col="blue", lwd="1", main="Graph #1", type="l")
lines(x, func7(x), col="red")
points(rt$root, rt$root, pch=16, cex=2, col="red")

As pointed out by K.Troy, in the general case the y-coordinate should be transformed : "The second argument to the points function should be to invoke either func6 or func7 using rt$root"

points(rt$root, func6(rt$root), pch=16, cex=2, col="red")

Upvotes: 1

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