f(x)=ax^3-2ax^2+b (a>0)在区间【-2,1】上最大值是5,最小值是-11 求f(x)的解析式

f(x)=ax^3-2ax^2+b (a>0)
f'(x) = 3ax^2-4ax = 3ax(x-4/3)
x∈【-2,0）时,f'(x) ＞0,f(x)单调增；
x∈(0,1）时,f'(x) ＜0,f(x)单调减
x=0时,有最大值f(0) = 0-0+b = 5,b=5
f(x)=ax^3-2ax^2+5
f(-2) = -8a-8a+5 = -16a+5
f(1) = a-2a+5 = -a+5
假设最小值f(-2) = -16a+5 = -11,a=1
假设最小值f(1) = -a+5 = -11,a=16
∴f(x)=x^3-2x^2+5,或f(x)=16x^3-32x^2+5