       Re: Manipulate (from Wolfram Demonstrations)

• To: mathgroup at smc.vnet.net
• Subject: [mg76869] Re: Manipulate (from Wolfram Demonstrations)
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Tue, 29 May 2007 04:53:12 -0400 (EDT)
• References: <f3bhf0\$3cr\$1@smc.vnet.net>

```Bruce Colletti wrote:
> Re Mathematica 6.0 under WinXP.
>
> The code below (from Wolfram Demonstrations site) plots a tangent at the point set by the slider.
>
> Point[{xi,p}] baffles me:  Point requires two numbers, but p is a function...I don't see how it evaluates to a number AT THIS location in the Manipulate statement.
>
> What is the mechanism that makes p evaluate to a number?  Is it somehow referring to Plot's {x,-2,2} ?
>
> Thankx.
>
> Bruce
>
> Manipulate[
>  With[{p = a x^3 + b x^2 + c x, dx = .8},
>   With[{pp = D[p, x]},
>    Plot[p, {x, -2, 2}, Ticks -> None, PlotRange -> All,
>     Epilog -> ({Orange, PointSize[.02], Point[{xi, p}],
>         Thickness[.005],
>         Line[{{xi - dx, p - dx pp}, {xi + dx, p + dx pp}}]} /.
>        x -> xi)]]], {{xi, 0, Subscript[x, 0]}, -2,
>   2}, Delimiter, {{a, -2, "a"}, -2, 2}, {{b, -2, "b"}, -2,
>   2}, {{c, -2, "c"}, -2, 2}, ControllerLinking -> True]
>

Technically, p is not a function here, but an expression involving the
variable x. Thus the Plot command contains an expression that depends on
x, and is analogous to the archetypal Plot[Sin[x],{x,0,10}]

David Bailey
http://www.dbaileyconsultancy.co.uk

```

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