a question on differentiability
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From: dushya on 1 Jun 2010 09:32 suppose f:A->B ; g:A->C and h:C->B be such that f = hog by composite function theorem if h and g are differentiable then so is f but does differentiability of f and g imply differentiability of h ? or does differentiability of f and h imply differentiability of g ? please reply.
From: Alois Steindl on 1 Jun 2010 09:38 dushya <sehrawat.dushyant(a)gmail.com> writes: > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > by composite function theorem if h and g are differentiable then so is > f but does differentiability of f and g imply differentiability of h ? > or does differentiability of f and h imply differentiability of g ? > > please reply. Hello, if this is a homework example, try to find a counterexample. Alois -- Alois Steindl, Tel.: +43 (1) 58801 / 32558 Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598 Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10
From: dushya on 1 Jun 2010 09:50 On Jun 1, 6:38 am, Alois Steindl <Alois.Stei...(a)tuwien.ac.at> wrote: > dushya <sehrawat.dushy...(a)gmail.com> writes: > > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > > by composite function theorem if h and g are differentiable then so is > > f but does differentiability of f and g imply differentiability of h ? > > or does differentiability of f and h imply differentiability of g ? > > > please reply. > > Hello, > if this is a homework example, try to find a counterexample. > Alois > > -- > Alois Steindl, Tel.: +43 (1) 58801 / 32558 > Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598 > Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10 no its not homework!! i encountered this problem in learning about fibre bundles. and i was not able to think of any counter-examples. and i am a physics student. its been years when i last studied some analysis.
From: Ron on 1 Jun 2010 10:03 On Jun 1, 9:32 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > by composite function theorem if h and g are differentiable then so is > f but does differentiability of f and g imply differentiability of h ? > or does differentiability of f and h imply differentiability of g ? > > please reply. Hint: Consider constant functions.
From: dushya on 1 Jun 2010 10:13
On Jun 1, 7:03 am, Ron <ron.sper...(a)gmail.com> wrote: > On Jun 1, 9:32 am, dushya <sehrawat.dushy...(a)gmail.com> wrote: > > > suppose f:A->B ; g:A->C and h:C->B be such that f = hog > > > by composite function theorem if h and g are differentiable then so is > > f but does differentiability of f and g imply differentiability of h ? > > or does differentiability of f and h imply differentiability of g ? > > > please reply. > > Hint: Consider constant functions. hey thanks :-) but suppose we have two more conditions g(A)=C, f(A)=B. |