Re: Why can't Mathematica find this root?
- To: mathgroup at smc.vnet.net
- Subject: [mg38327] Re: Why can't Mathematica find this root?
- From: atelesforos at hotmail.com (Orestis Vantzos)
- Date: Thu, 12 Dec 2002 01:35:45 -0500 (EST)
- References: <at4dgq$f1c$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
f'[x] is a periodic function, hence it has an infinity of roots. Mathematica tries to sample at least one period of this function; in this case it returns roots contained in the (-Pi,Pi) interval. Since the period of the function is Pi, it can be deduced that x->0 also corresponds to x->Pi (actually x->k*Pi, with k in the Integers). Since Solve produces a relevant message, I think its overall behaviour is consistent in this case. Orestis Vantzos "Konrad Den Ende" <konrad at voxway.com> wrote in message news:<at4dgq$f1c$1 at smc.vnet.net>... > Regard this function: > > f[x_] := Sin[x]^3 * Cos[x] > > And then try this: > > Solve[f'[x] == 0, x] > > and you'll get a list of all roots but one. I wonder why. > > By regarding f'[x] one can directly see that x = pi is a root, > > yet, Mathematica fails to see it... > > > Vänligen > Konrad > -------------------