a) Es ist

${\displaystyle {}f(0)=B_{0}(0)v_{0}+B_{1}(0)v_{1}+B_{2}(0)v_{2}=v_{0}\,}$

und

${\displaystyle {}f(1)=B_{0}(1)v_{0}+B_{1}(1)v_{1}+B_{2}(1)v_{2}=v_{2}\,.}$

b) Es ist

${\displaystyle {}{\begin{aligned}f'(t)&=B_{0}'(t)v_{0}+B_{1}'(t)v_{1}+B_{2}'(t)v_{2}\\&={\left(2t-2\right)}v_{0}+{\left(-4t+2\right)}v_{1}+{\left(2t\right)}v_{2}.\end{aligned}}}$

c) Es ist

${\displaystyle {}f'(0)=-2v_{0}+2v_{1}=2{\left(v_{1}-v_{0}\right)}\,}$

und

${\displaystyle {}f'(1)=-2v_{1}+2v_{2}=2{\left(v_{2}-v_{1}\right)}\,.}$