R help - Oct 2011 - An issue regarding to gradient

The following code will get me a curve plot:
cutoff <- seq(1,7,0.25)
Sensitivity <- 1 - pnorm(cutoff, 5, 0.8)
Specificity <- pnorm(cutoff, 3, 1.2)
plot(1-Specificity,Sensitivity,main = "ROC curve",type =
"o")

How do I get a gradient of a particular point on that curve?
Any packages/functions allow me to do that?  

Thank you

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On Oct 11, 2011, at 6:02 AM, luke1022 wrote:
> The following code will get me a curve plot:
> cutoff <- seq(1,7,0.25)
> Sensitivity <- 1 - pnorm(cutoff, 5, 0.8)
> Specificity <- pnorm(cutoff, 3, 1.2)
> plot(1-Specificity,Sensitivity,main = "ROC curve",type =
"o")
>
> How do I get a gradient of a particular point on that curve?
First you need to define what you mean by "gradient at a point" when  
the gradient is discontinuous at each point. Is this a numerical  
example and you want to take the means of the slopes on either side,  
(rather like the definition of the Dirac function at x=0) ...

in whiich case these are the  slopes _between_not_at_ the points:

diff(Specificity)/diff(1-Sensitivity)

or ... is this a homework problem and you are being asked to use the  
knowledge that those (Sensitivity, Specificity) points came from  
particular pnorm functions?

-- 

David Winsemius, MD
West Hartford, CT