Question

f(x）g(x)在区间[a,b]上都有意义，

f(x）g(x)在区间[a,b]上都有意义，其在此区间上满足f(x)为增函数且f(x)〉0，g(x)为减函数且g(x)〈0，判断f(x)*g(x)在区间[a,b]上的单调性
快~~~~~`过程~~~~~

Answer 1

设a<=x1<x2<=b
则 0<f(x1)<f(x2) , 0>g(x1)>g(x2)
所以g(x2)*f(x2)<g(x1)*f(x2)

f(x2)*g(x2)-f(x1)*g(x1)
< f(x2)*g(x1)-f(x1)*g(x1)
= [f(x2)-f(x1)]*g(x1)
f(x2)-f(x1)>0
g(x1)<0

所以 f(x2)*g(x2)-f(x1)*g(x1)<0
f(x)*g(x)在区间[a,b]上为减函数