When does $y=kx^3-(k+1)x^2+(2-k)x-k$ have a minimum at $x =1$?

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The cubic \[y=kx^3-(k+1)x^2+(2-k)x-k\]

has a turning point, that is a minimum, when \(x = 1\) precisely for

\[\text{(a)} \quad k>0, \quad \text{(b)} \quad 0<k<1, \quad \text{(c)} \quad k > \dfrac{1}{2}, \quad \text{(d)} \quad k < 3, \quad \text{(e) all values of } x.\]