No sign change found error in R but not excel - r

Question

Just trying to understand why when I find the root of the following equation in excel I get a value however in R I get the "no sign change found error"
(-exp(-i*x))-x + 1
i = 1 in this case.
I'm plotting a graph where the value for i is 1:5. I've done this manually on excel and got a value of 0.003 when i = 1, here is the graph for all values of i: image 1
When try to find the root for when i = 1 in R though I get the error.
This is the code I am using to find the root:
func1 <- function(x) {
(-exp(-1*x))-x+1
}
root <- uniroot(func1, lower =0.5, upper = 1, extendInt = "yes")
print(root)
print(root$root)
}
Plotting the equation when i = 1 gives the following curve: image 2
Looking at the curve it doesn't seem like f(x) crosses 0 which explains the error, however, I get a value in excel.
Any help on this would be really appreciated
Thanks

Answer 1

This is the best I can offer. It is using a method of derivatives I found at http://rpubs.com/wkmor1/simple-derivatives-in-r. It will allow you to get the roots from newtons method.
options(scipen = 999)
f<-function(x) (-exp(-x)-x+1)
g<-function(x) { }
body(g)<-D(body(f),"x")
x <- 19
y<-vector()
y[1]<-x
for(i in 2:500) {
y<-c(y, y[i-1] - (f(y[i-1])/g(y[i-1])))
if(y[i]==y[i-1]) break
}
y
The output looks like this:
> y
[1] 19.000000000000000 0.999999893546867 0.418023257075328 0.194491909332762
[5] 0.094095681658666 0.046310116577025 0.022976345768161 0.011444180565743
[9] 0.005711176200954 0.002852869974152 0.001425756748278 0.000712708975595
[13] 0.000356312158327 0.000178145499021 0.000089070105497 0.000044534390909
[17] 0.000022267031356 0.000011133470771 0.000005566723944 0.000002783342584
[21] 0.000001391644148 0.000000695821730 0.000000347990248 0.000000173795172
[25] 0.000000086916841 0.000000043487300 0.000000023063442 0.000000013435885
[29] -0.000000003090351 -0.000000003090351
I hope this helps.