1. ## function 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

2. Originally Posted by Asak
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).

CB

3. 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

Asak