I have a question on cyclic subspaces.

V is a finite dimensional space over the field F. There exists f:V->V

It's given to me that , k is minimal, such that the set $(v,f(v),f^2(v),...,f^k(v))$ is dependent.

Now I have to prove that

1-)$D=(v,f(v),f^2(v),...,f^(k-1))$

2-)D spans Z(v,f)

I proved the first one which was very easy. But I am having a problem proving that it spans the cyclic subspace... Can someone give me a direction. Thanks