已知函数f(X)=-(1/3)x^3+2ax^2-3(a^2)x(a不等于0）当a>0时求函数y=f(x)的单调区间和极值

f(x)=-(1/3)x^3+2ax^2-3(a^2)x
f'(x)=-x^2+4ax-3a^2=-(x-3a)(x-a)=0
x=3a或x=a
∵a>0
∴3a>a
单调增区间(-∞,a],[3a,+∞)
单调减区间[a,3a]
极大值f(a)=-4a^3/3
极小值f(3a)=0