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

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

How can we find the turning points on a graph?

How can we find out what kind of turning points they are?