证明函数y=ln(1+1/x)在(0,正无穷)上单调递减
问题描述：
证明函数y=ln(1+1/x)在(0,正无穷)上单调递减
答
令x2>x1>0
ln(1+1/x2)-ln(1+1/x1)
=ln[(1+1/x2)/(1+1/x1)]
=ln[(x1x2+x1)/(x1x2+x2)]
∵x2>x1>0
∴0
答
y' = (1 + 1/x)(-1/x²) = -(x + 1)/x³
x > 0,x³ > 0,x + 1 > 0,y' = -(x + 1)/x³