Let \(f\) be any continuous function on \([0,2]\) and twice differentiable on \((0,2)\). If \(f(0)=0, f(1)=1\) and \(f(2…

\(f^{\prime \prime}(x)=0\) for all \(x \in(0,2)\)

\(f^{\prime \prime}(x)>0\) for all \(x \in(0,2)\)

\(f^{\prime}(x)=0\) for some \(x \in[0,2]\)

\(f^{\prime \prime}(x)=0\) for some \(x \in(0,2)\)