first and second derivative calculation

D(expression(t^3-6*t^2+5*t + 30), 't')

D(D(expression(t^3-6*t^2+5*t + 30), 't'), 't')

I can plot this just fine:
t<-seq(0,4, by=.1)
y<- t^3-6*t^2+5*t+30
plot(t,y ,xlab="t-values", ylab="f(t)", type="l")
This is the first derivative, how I I make a similar plot?
t<-seq(0,4, by=.1)
y<- t^3-6*t^2+5*t+30
y1<-D(expression(t^3-6*t^2+5*t+30), 't')

-- 

Thanks ahead of time.

kc


On Fri, Jan 22, 2010 at 12:41 PM, Doran, Harold <HDoran at air.org>  
wrote:

D(expression(t^3-6*t^2+5*t + 30), 't')

3 * t^2 - 6 * (2 * t) + 5

D(D(expression(t^3-6*t^2+5*t + 30), 't'), 't')

3 * (2 * t) - 6 * 2

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org 
]
On Behalf Of Marlin Keith Cox
Sent: Friday, January 22, 2010 4:37 PM
To: r-help at r-project.org
Subject: [R] first and second derivative calculation

I would like to calculate a first and second derivative and am having
problems finding a simple solution.  My syntax may be off as I am  
not a
mathematician, so pardon ahead of time.
data:
t<-seq(0,4, by=.1)
The function is:
H(t) = t^3-6*t^2+5*t + 30

from here I plot the curve:
plot(x,y ,xlab="x-values", ylab="f(x)", type="l")
But would like to similarly plot the curve for both the first and  
second
derivatives.
I can calculate the derivatives by hand but would like to get R to  
do this
for me.
by hand:
H'(t) = 3*t^2 - 12*t + 5
H''(t) = 6*t-12
Keith

--
M. Keith Cox, Ph.D.
Alaska NOAA Fisheries, National Marine Fisheries Service
Auke Bay Laboratories
17109 Pt. Lena Loop Rd.
Juneau, AK 99801
Keith.Cox at noaa.gov
marlinkcox at gmail.com
U.S. (907) 789-6603

      [[alternative HTML version deleted]]

-- 
M. Keith Cox, Ph.D.
Alaska NOAA Fisheries, National Marine Fisheries Service
Auke Bay Laboratories
17109 Pt. Lena Loop Rd.
Juneau, AK 99801
Keith.Cox at noaa.gov
marlinkcox at gmail.com
U.S. (907) 789-6603

	[[alternative HTML version deleted]]

On Jan 22, 2010, at 6:49 PM, Marlin Keith Cox wrote:

I can plot this just fine:
t<-seq(0,4, by=.1)
y<- t^3-6*t^2+5*t+30
plot(t,y ,xlab="t-values", ylab="f(t)", type="l")
This is the first derivative, how I I make a similar plot?
t<-seq(0,4, by=.1)
y<- t^3-6*t^2+5*t+30
y1<-D(expression(t^3-6*t^2+5*t+30), 't')

There might be some sort of deparse() operation that one could do on  
y1, but what follows sidesteps that level of programming.


y1fn <- function(t) {3 * t^2 - 6 * (2 * t) + 5}
par(new=TRUE)
plot(t, y1fn(t), ylab="", xlab="", axes=FALSE)
  axis(side=4, at=seq(-7,5,by=1) )

-- 

David.

Thanks ahead of time.

kc


On Fri, Jan 22, 2010 at 12:41 PM, Doran, Harold <HDoran at air.org>  
wrote:

D(expression(t^3-6*t^2+5*t + 30), 't')

3 * t^2 - 6 * (2 * t) + 5

D(D(expression(t^3-6*t^2+5*t + 30), 't'), 't')

3 * (2 * t) - 6 * 2

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org 
]
On Behalf Of Marlin Keith Cox
Sent: Friday, January 22, 2010 4:37 PM
To: r-help at r-project.org
Subject: [R] first and second derivative calculation

I would like to calculate a first and second derivative and am having
problems finding a simple solution.  My syntax may be off as I am  
not a
mathematician, so pardon ahead of time.
data:
t<-seq(0,4, by=.1)
The function is:
H(t) = t^3-6*t^2+5*t + 30

from here I plot the curve:
plot(x,y ,xlab="x-values", ylab="f(x)", type="l")
But would like to similarly plot the curve for both the first and  
second
derivatives.
I can calculate the derivatives by hand but would like to get R to  
do this
for me.
by hand:
H'(t) = 3*t^2 - 12*t + 5
H''(t) = 6*t-12
Keith

--
M. Keith Cox, Ph.D.
Alaska NOAA Fisheries, National Marine Fisheries Service
Auke Bay Laboratories
17109 Pt. Lena Loop Rd.
Juneau, AK 99801
Keith.Cox at noaa.gov
marlinkcox at gmail.com
U.S. (907) 789-6603

      [[alternative HTML version deleted]]

-- 
M. Keith Cox, Ph.D.
Alaska NOAA Fisheries, National Marine Fisheries Service
Auke Bay Laboratories
17109 Pt. Lena Loop Rd.
Juneau, AK 99801
Keith.Cox at noaa.gov
marlinkcox at gmail.com
U.S. (907) 789-6603

	[[alternative HTML version deleted]]

David Winsemius, MD
Heritage Laboratories
West Hartford, CT