Re: Find max of a Find root function

*To*: mathgroup at smc.vnet.net*Subject*: [mg113761] Re: Find max of a Find root function*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 11 Nov 2010 06:09:16 -0500 (EST)

Your e-mail appears to have been garbled, but everything works after fixing that. Start with a fresh kernel. f[a_?NumberQ] := x /. Last[FindRoot[x == Cos[a x], {x, .4}]] f[3] 0.39004 Plot[f[x], {x, 2, 3}] FindMaximum[{f[a], 2 <= a <= 3}, {a, 3}] {0.514933, {a -> 2.}} FindMaximum[{f[a], 2 <= a <= 3}, a] {0.514933, {a -> 2.}} NMaximize[{f[a], 2 <= a <= 3}, a] {0.514933, {a -> 2.}} I recommend that you use NumericQ rather than NumberQ NumberQ /@ {Pi, E, GoldenRatio} {False, False, False} NumericQ /@ {Pi, E, GoldenRatio} {True, True, True} Bob Hanlon ---- "Van Peursem wrote: ============= Can someone please assist me with the following sample problem. Bottom line is that I'd like to use the FindRoot function to numerically solve an equation, that involves a parameter. I'd then like to use the Findmax function that would yield the largest root for a specified range of the parameter. Any help would be appreciated. Thanks Dan I first define the function f[a_?NumberQ]:=x/.Last[FindRoot[xSCos[a x],{x,.4}]] and it evaluates nicely. f[3] 0.39004 It even graphs nicely. Plot[f[x],{x,2,3}] [cid:image002.png at 01CB8019.CA736910] But it doesn't like me asking for a max... FindMaximum[{f[a],2=A3a=A33},{a,3}] The errors I get are the following FindRoot::nlnum : The function value {1. -1. Cos[1. a]} is not a list of numbers with dimensions {1} at {x} = {1.}. ? ReplaceAll::reps : {FindRoot[xSCos[a x],{x,1}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. ? FindRoot::nlnum : The function value {1. -1. Cos[1. a]} is not a list of numbers with dimensions {1} at {x} = {1.}. ? ReplaceAll::reps : {FindRoot[xSCos[a x],{x,1}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. ? FindRoot::nlnum : The function value {1. -1. Cos[1. a]} is not a list of numbers with dimensions {1} at {x} = {1.}. ? General::stop : Further output of FindRoot::nlnum will be suppressed during this calculation. ? ReplaceAll::reps : {FindRoot[xSCos[a x],{x,1}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. ? General::stop : Further output of ReplaceAll::reps will be suppressed during this calculation. ? {-0.887727,{a=AE3.}}