MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Solve transcendental functions

  • To: mathgroup at
  • Subject: [mg21138] Re: Solve transcendental functions
  • From: Daniel Lichtblau <danl at>
  • Date: Fri, 17 Dec 1999 01:21:38 -0500 (EST)
  • Organization: Wolfram Research, Inc.
  • References: <831v41$>
  • Sender: owner-wri-mathgroup at

sandmann at wrote:
> If i got the function
> f[x]:=x^2-2Cos[a*x]/a
> and tries to Solve[f[x]==f'[x],x]
> I get
> The equations appear to involve transcendental functions of the
> variables in an essentially non-algebraic way.
> How do I solve this problem ?
> Regards Niels Sandmann
> Sent via
> Before you buy.

You can find solutions for particular values of a, provided you supply a
starting point for a Newton-type iteration.

f[x_,a_] := x^2-2Cos[a*x]/a
parametrizedSolve[f_, a_?NumberQ, init_] :=
	FindRoot[Evaluate[f[x,a]==D[f[x,a],x]], {x,init},
	AccuracyGoal->15, WorkingPrecision->20]

For example, if I want to handle the case where a is 1, starting near
x=2, I can do as below.

In[110]:= parametrizedSolve[f, 1, 2]
Out[110]= {x -> 2.1999981850434100730}

Starting at x=0 gives

In[111]:= parametrizedSolve[f, 1, 0]
Out[111]= {x -> -0.41895202574023425297}

Daniel Lichtblau
Wolfram Research

  • Prev by Date: Re: Graphics3D[] objects clipping & PlotRange
  • Next by Date: Re: question
  • Previous by thread: Re: Solve transcendental functions
  • Next by thread: Re: Solve transcendental functions