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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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
Put g(x)=xf(x), and show that x=1 gives a global maximum of g(x).Quote:
Originally Posted by Asak
CB
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