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]

**Follow-Ups**:**Re: Manipulate (from Wolfram Demonstrations)***From:*Murray Eisenberg <murray@math.umass.edu>