Re: Why can't Mathematica find this root?
- To: mathgroup at smc.vnet.net
- Subject: [mg38304] Re: Why can't Mathematica find this root?
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Thu, 12 Dec 2002 01:31:35 -0500 (EST)
- References: <at4dgq$f1c$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Konrad Den Ende" <konrad at voxway.com> wrote: > 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. No, you don't. There are infinitely many roots, of which Mathematica gives you only three: -Pi/2, 0, and Pi/2. > I wonder why. Didn't you notice Mathematica's comment that, since inverse functions were being used, some solutions might not be found? That's the explanation. > By regarding f'[x] one can directly see that x = pi is a root, > > yet, Mathematica fails to see it... More basically, just try Solve[Sin[x] == 0, x]. The only solution you'll get is 0, the _principal_ value of the inverse sine of 0. David -- -------------------- http://NewsReader.Com/ -------------------- Usenet Newsgroup Service New Rate! $9.95/Month 50GB