Re: Manipulate (from Wolfram Demonstrations)

*To*: mathgroup at smc.vnet.net*Subject*: [mg76822] Re: [mg76774] Manipulate (from Wolfram Demonstrations)*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Mon, 28 May 2007 00:56:34 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200705270853.EAA03281@smc.vnet.net>*Reply-to*: murray at math.umass.edu

The value of p is not really a function, but rather the expression a x^3 + b x^2 + c x involving x. And in the Epilog, the phrase "/. x -> xi" applies to the part of the expression that includes Point[{xi,p}]. Thus the value of x in a x^3 + b x^2 + c x is replaced by xi. 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] > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Manipulate (from Wolfram Demonstrations)***From:*Bruce Colletti <vze269bv@verizon.net>