Re: Plotting a function and its derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg49487] Re: Plotting a function and its derivative*From*: BobHanlon at aol.com*Date*: Thu, 22 Jul 2004 02:44:51 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

f[x_] := x^2; d[x_] := Evaluate[D[f[x], x]]; Plot[{f[x],f'[x]},{x,0,2}]; Plot[{f[x],d[x]},{x,0,2}]; d[3]==f'[3] True Bob Hanlon > In a message dated Wed, 21 Jul 2004 11:17:20 +0000 (UTC), < > skaai at earthlink.net> writes: 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_] := =B6_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 > > > anyways, to simplify my question, how to i plot a function (like x^2) > and its derivative (like 2x) and apply its derivative to any part of > the function (like x=3) so as to show the tangent line which should > touch the function? i thought my way should have worked, but it seems > the d(x) is the troublesome function, since without it, i get a graph > of the function (albeit without the derivative)..... >