Re: Issuing Function Calls within a Plot command

*To*: mathgroup at smc.vnet.net*Subject*: [mg111518] Re: Issuing Function Calls within a Plot command*From*: "David Park" <djmpark at comcast.net>*Date*: Wed, 4 Aug 2010 05:48:03 -0400 (EDT)

The reason you obtain nothing is that Plot has the Attribute HoldFirst, which means that the plot expression is not immediately evaluated. Instead, Mathematica substitutes x values into it and only then evaluates. So say that Mathematica evaluates at x = 0.1. Then the plot expression becomes D[myFunction[0.1],0.1], which makes no sense and will not return a value. The solution is to tell Mathematica to evaluate the derivative first. myFunction[x_] := x^2; Plot[D[myFunction[x], x] // Evaluate, {x, 0, 5}] In this case, there is an even simpler construction. Plot[myFunction'[x], {x, 0, 5}] If you had a function with parameters, defined as f[a_,b_][x_]:= expression in a, b and x, then you could use f[2,3]`[x] say as a plot function of the derivative with specific parameters. If you have a plot function that involves complicated processing, such as Integral, then it is worthwhile to define the plot function outside of any Plot statement and make certain you know what you are dealing with - by looking at the resulting expression, or evaluating at some points, or looking at it with Table. This untangles the plot function definition from the plotting algorithm and simplifies any debugging. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Andrew DeYoung [mailto:adeyoung at andrew.cmu.edu] Hi, It seems like Mathematica has difficulty plotting calls to other functions. Is this true? For example, can you help me understand why the following does not plot? If I write myFunction[x_] := x^2; Plot[D[myFunction[x], x], {x, 0, 5}] nothing plots. If I write myFunction[x_] := x^2; Plot[D[myFunction[x][x], x], {x, 0, 5}] again, nothing plots. However, if I compute the derivative of the function outside of the Plot command, myFunction[x_] := x^2; myDerivative = D[myFunction[x], x] Plot[myDerivative, {x, 0, 5}] the derivative of x^2 (i.e., 2x) plots correctly. Can anyone please help me understand why my first two tries do not work, but my third try does? Many thanks in advance. Andrew DeYoung Carnegie Mellon University adeyoung at andrew.cmu.edu