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My attempt: I have computed $Rf'(1)=c$ and $Lf'(1)=2a.$ Now for $f'$ to be continuous ,we must have , $c=2a$ . But I am not sure how to find $b$?Also,where should I use the fact that $f$ is increasing in $(0,\infty)?$ Can someone point me in the right direction? please help.Thanks in advance for your time.

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Continuity of $f'$ at $1$ is simply equivalent to $c=2a$. No need to equate this with $f(1)$. And $f$ is increasing if and only if $2a>0$ and $c>0$. This leaves room, for infinitely many $(a,b,c)$. So D. –  1015 Feb 9 '13 at 15:48
@julien Thanks a lot.I have got it. –  user52976 Feb 9 '13 at 16:01

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