Re: Plotting a function and its derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg49529] Re: Plotting a function and its derivative*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Thu, 22 Jul 2004 02:47:10 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 7/21/04 at 6:40 AM, skaai at earthlink.net (adrian sky) wrote: >anyways, what i'm trying to do is illustrate the simplest of >derivatives in the form of a graph but i am getting errors. >the function i'm trying to derive is x^2 its derivative i'm trying >to illustrate is 2x >i would like to set up a graph which allows me to determine the >argument (be it x^2 or x^4+1), calculate its derivative, and graph >them so as to illustrate their relationship. >i know that the derivative can be graphed at any x value, and as >far as this is concerned, the value can be anything, probably a >small value to keep the graph manageable. >anyways, i'm inputting this: f[x_] := x^2; d[x_] := â??_x f[x] which >supposedly should assign the f(x) a value of ^2 and d(x) a value of >the derivative of f(x) >i can even type f(x) and get back the value x^2 and d(x) gives me >2x, so it seems the system understands and assigns the requested >values >but when I try to plot this with the command: Plot[{f[x], d[x]}, >{x, -5, 5}] i get numerous errors and only get the graph of x^2 the >errors are: General::ivar: -5. is not a valid variable. Plot::plnr: >d[x] is not a machine-size real number at x = -4.9999995833333335` >Plot::plnr: d[x] is not a machine-size real number at x = >-4.594330084270842` and a few more similar plot errors The problem you are having is due to the way Plot evaluates its arguements. What is happening is Plot sends your function d a numeric value and d attempts to take the derivative of a numeric value with respect to x. This is clearly not what you want. There are two ways around this. First, you can define d using Set rather than DelayedSet. That will cause the derviative to be evaluated before Plot tries to substitute a value for x. The second way would be to use Evaluate to force evaluation of the derivative before Plot substitutes values for x, i.e., with your d defined as is do: Plot[Evaluate@{f[x],d[x]}, {x, -5, 5}] Look at the discussion of Plot, Set and DelayedSet in the Mathematica Book for a more complete discussion. -- To reply via email subtract one hundred and four

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