Question

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）,则K的值是?

Answer 1

f'(x)=3kx^2+6(k-1)x=x(3kx+6k-6)=0的解为x1=0,x=(2-2k)/k,因为原函数减区间为(0,4),即f'(x)