Statement 1: If $f\left(x\right)$ is differentiable in $\left[0,1\right]$ such that $f\left(0\right)=f\left(1\right)=0,$ then for any $\lambda \in R,$ there exists $c$ such that $f^{p}rime$(c)$=\lambda$f(c),$0<c<1.$ statement 2: if $g\left(x\right)$ is differentiable in [0,1], where $g\left(0\right)=g\left(1\right),$ then there exists $c$ such that $g^{p}rime$(c)=0,

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