证明:首先设x1>x2>0,则
F(x1)-F(x2)=√(x1^2+1)-ax1-√(x^2+1)+ax2
=(x1^2-x2^2)/[√(x1^2+1)+√(x2^2+1)]-a(x1-x2)
=(x1-x2)[(x1+x2)/(√(x1^2+1)+√(x2^2+1))-a]x2>0,即x1-x2>0,
所以(x1+x2)/(√(x1^2+1)+√(x2^2+1))-ax1+x2>0
所以0
证明:首先设x1>x2>0,则
F(x1)-F(x2)=√(x1^2+1)-ax1-√(x^2+1)+ax2
=(x1^2-x2^2)/[√(x1^2+1)+√(x2^2+1)]-a(x1-x2)
=(x1-x2)[(x1+x2)/(√(x1^2+1)+√(x2^2+1))-a]x2>0,即x1-x2>0,
所以(x1+x2)/(√(x1^2+1)+√(x2^2+1))-ax1+x2>0
所以0