       Manipulate (from Wolfram Demonstrations)

• To: mathgroup at smc.vnet.net
• Subject: [mg76774] Manipulate (from Wolfram Demonstrations)
• From: Bruce Colletti <vze269bv at verizon.net>
• Date: Sun, 27 May 2007 04:53:37 -0400 (EDT)

```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]

```

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