Hello,

I've the following function :

f(x)=((1+(1-2*x/c)^0.5)*exp(-2*x/(1+(1-2*x/c)^0.5))-

-(1-(1-2*x/c)^0.5)*exp(-2*x/(1-(1-2*x/c)^0.5)))/(1-2*x/c)^0.5

where 1<x<c/2, c is a positive constant.

I've to show that f(1)>=x*f(x)

Any ideas ?

Asak

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- Dec 16th 2009, 03:47 AMAsakfunction properties
Hello,

I've the following function :

f(x)=((1+(1-2*x/c)^0.5)*exp(-2*x/(1+(1-2*x/c)^0.5))-

-(1-(1-2*x/c)^0.5)*exp(-2*x/(1-(1-2*x/c)^0.5)))/(1-2*x/c)^0.5

where 1<x<c/2, c is a positive constant.

I've to show that f(1)>=x*f(x)

Any ideas ?

Asak - Dec 16th 2009, 04:04 AMCaptainBlack
- Dec 16th 2009, 04:09 AMAsak
Hi,

I've tried to do that, but the derivative is a horror and I can't show that

g(x)=xf(x) is a decreasing function (Worried)

Asak