已知函数f(x)=kx^3+3(k-1)x^2-k^2+1(k

已知函数f(x)=kx^3+3(k-1)x^2-k^2+1(k<0)的单调减区间是（0,4）,求k
解析：∵函数f(x)=kx^3+3(k-1)x^2-k^2+1
f’(x)=3kx^2+6(k-1)x=0
x1=0
f”(x)=6kx+6(k-1)==> f”(0)=6(k-1)<0==>k<1
x2=2(1-k)/k=4==>k=1/3
∴k=1/3