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Benko
Frequent VisitorJoined: 16 Jul 2004Posts: 33
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Posted: Sun Dec 12, 2004 8:03 pm Post subject: inequality
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For x>-1,what is the minimun value of (x^2+1)/(x+1)?
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Tc
Frequent VisitorJoined: 25 Oct 2003Posts: 135
Location: Hong Kong
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Posted: Sun Dec 12, 2004 8:16 pm Post subject:
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Topic moved to High School Maths
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Wilson
Frequent VisitorJoined: 20 Oct 2004Posts: 74
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Posted: Mon Dec 13, 2004 10:42 am Post subject: Re: inequality
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Let f(x)=(x^2+1)/(x+1) f(x)=x-1+2/(x+1) f'(x)=1-2/(x+1)^2=0 when x=-1+root2 since x>-1 f”(x)=4/(x+1)^3>0 => minimum point
Minimum value of f=f(-1+root2)=(4-2root2)/root2=2root2-2
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