求证:函数f(x)=-1/x-4在区间(负无穷,0)上是单调增函数.

Question

求证:函数f(x)=-1/x-4在区间(负无穷,0)上是单调增函数.

Answer 1

证明：在(-∞,0)上取x1,x2(x1＜x2)f(x1)-f(x2)=-1/x1-4-(-1/x2-4)=1/x2-1/x2=(x1-x2)/x1x2∵x1＜x2,且x1,x2都为负数∴x1-x2＜0 x1x2＞0∴(x1-x2)/x1x2＜0即f(x1)-f(x2)＜0∴f(x1)＜f(x2)∴函数f(x)=-1/x-4在(-∞,0)...