Re: Log(ln) Function + 2 Parameters + Greater

• To: mathgroup at smc.vnet.net
• Subject: [mg89298] Re: Log(ln) Function + 2 Parameters + Greater
• From: Jerry <Jer75811 at yahoo.com>
• Date: Wed, 4 Jun 2008 05:37:38 -0400 (EDT)
• References: <g22tp5\$ikl\$1@smc.vnet.net> <g237c4\$q2n\$1@smc.vnet.net>

```Sir, I have never seen a function definition in the form you
give:
f[a_][x_] := x (a + Log[x])^2

After a bit of playing with it, I don't see the difference
between this and

f[a_,x_] := x (a + Log[x])^2

I really don't know how to search in help for this f[a_][x_]
form. Can you tell me if there is any essential difference?

Thank you.

David Park wrote:
> First, define your f function with a as a parameter.
>
> f[a_][x_] := x (a + Log[x])^2
>
> Mathematica can't make a plot unless it knows values for a. Of course, it
> won't plot any results for x < 0 and I'm not certain if you actually meant x
>  > 0 rather than a > 0. In any case, you can use any real domain for a. Here
> is a plot for a specific value of a.
>
> Plot[f[2][x], {x, -5, 5},
>  AxesLabel -> {x, f}]
>
> You can look at an extended a domain by using Plot3D.
>
> Plot3D[f[a][x], {a, -5, 5}, {x, 0, 5},
>  PlotRange -> All,
>  AxesLabel -> {a, x, f}]
>
> Another approach is to use a Manipulate statement with a controlled by a
> slider.
>
> Manipulate[
>  Plot[f[a][x], {x, 0, 5},
>   PlotRange -> {0, 250},
>   AxesLabel -> {x, f}],
>  Style[Row[{HoldForm[f["a"][x]] == f["a"][x]}], 16],
>  Delimiter,
>  {a, -5, 5, Appearance -> "Labeled"}]
>
>
>

```

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