Re: FindRoot and replacement rule
- To: mathgroup at smc.vnet.net
- Subject: [mg123925] Re: FindRoot and replacement rule
- From: Helen Read <readhpr at gmail.com>
- Date: Fri, 30 Dec 2011 07:08:26 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jdh68h$kjj$1@smc.vnet.net>
It's useful if you want to substitute the solutions into a function. For example, suppose you want to find point(s) of intersection. f[x_] := 8 x^2 - 12 x + 5 g[x_]:=26 - 10 x {x, f[x]} /. Solve[f[x] == g[x], x] Here's another way that I use it all the time, when I'm rigging up functions for my calculus students (for example when we are doing area or volume problems etc.). Make up a function that looks nice: f[x_] := x^4 - 2 x^3 + 5 Say I want a parabola that will intersect f[x] at let's say x=-3/2 and x=2. I'll need another point to determine the parabola, so plot f[x] and pick something that will make it look nice. Let's say I want the parabola to go through (1,15). Now I start with a generic parabola, here called gg[x]. My final parabola will be g[x], which I get by solving for the values of a, b, and c in gg[x] and then evaluating gg[x] using the substitution rules from Solve. gg[x_] := a x^2 + b x + c g[x_] = gg[x] /. Solve[{gg[-3/2] == f[-3/2], gg[2] == f[2], gg[1] == 15}, {a, b, c}][[1]] The [[1]] is picking out the first solution (there is in fact only one, but Solve returns a list of solutions). Helen Read University of Vermont On 12/29/2011 2:52 AM, SamTakoy wrote: > Hi, > > Just wondering why FindRoot and other solvers return substitution > rules rather than simply a list of solutions. What's the advantage? > > Thanks! > > Sam >