这道数学题目的解题步骤过程！(步骤详细)
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f(x)=ax/(x+r)^2,定义域：x≠-r
f'(x)=a/(x+r)^2-2ax/(x+r)^3=[a(x+r)-2ax]/(x+r)^3=-a(x-r)/(x+r)^3
(1-i)r=0,a>0,x≠0,f'(x)<=0,
(1-ii)r=0,a<0,x≠0,f'(x)>=0
(2-i)r>0,a<0,(x-r)/(x+r)>=0,x>=r或x<-r,f'(x)>=0
(2-ii)r>0,a<0,(x-r)/(x+r)<=0,-r<x<=r,f'(x)<=0
(2-iii)r>0,a>0,(x-r)/(x+r)<=0,-r<x<=r,f'(x)>=0
(2-iiii)r>0,a>0,(x-r)/(x+r)>=0,x>=r或x<-r,f'(x)<=0
(3-i)r<0,a<0,(x-r)/(x+r)>=0,x>-r或x<=r,f'(x)>=0
(3-ii)r<0,a<0,(x-r)/(x+r)<=0,r<=x<-r,f'(x)<=0
(3-iii)r<0,a>0,(x-r)/(x+r)<=0,r<=x<-r,f'(x)>=0
(3-iiii)r<0,a>0,(x-r)/(x+r)>=0,x>-r或x<=r,f'(x)<=0
f'(x)=a/(x+r)^2-2ax/(x+r)^3=[a(x+r)-2ax]/(x+r)^3=-a(x-r)/(x+r)^3
(1-i)r=0,a>0,x≠0,f'(x)<=0,
(1-ii)r=0,a<0,x≠0,f'(x)>=0
(2-i)r>0,a<0,(x-r)/(x+r)>=0,x>=r或x<-r,f'(x)>=0
(2-ii)r>0,a<0,(x-r)/(x+r)<=0,-r<x<=r,f'(x)<=0
(2-iii)r>0,a>0,(x-r)/(x+r)<=0,-r<x<=r,f'(x)>=0
(2-iiii)r>0,a>0,(x-r)/(x+r)>=0,x>=r或x<-r,f'(x)<=0
(3-i)r<0,a<0,(x-r)/(x+r)>=0,x>-r或x<=r,f'(x)>=0
(3-ii)r<0,a<0,(x-r)/(x+r)<=0,r<=x<-r,f'(x)<=0
(3-iii)r<0,a>0,(x-r)/(x+r)<=0,r<=x<-r,f'(x)>=0
(3-iiii)r<0,a>0,(x-r)/(x+r)>=0,x>-r或x<=r,f'(x)<=0
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