Limits Continuity And Differentiability

Let \(f(x)=2+\cos x\) for all real \(x\).

STATEMENT - 1 : For each real \(t\), there exists a point \(c\) in \([t, t+\pi]\) such that \(f^{\prime}(C)=0\).

STATEMENT - 2 : \(f(t)=f(t+2 \pi)\) for each real \(t\).