Proof of Rolle's Theorem

Q. Let $y=f\left(x\right)\text{and}y=g\left(x\right)$ be two differentiable function in $[0,2]$ such that $f\left(0\right)=3,f\left(2\right)=5,g\left(0\right)=1\text{and}g\left(2\right)=2.$ If there exists atleast one $cϵ(0,2)$ such that $f^{\prime }\left(c\right)=k{g}^{\prime }\left(c\right)$, then $k$ must be

1. 2
2. 3
3. $\frac{1}{2}$
4. 1

Q. Let $y=f\left(x\right)\text{and}y=g\left(x\right)$ be two differentiable function in $[0,2]$ such that $f\left(0\right)=3,f\left(2\right)=5,g\left(0\right)=1\text{and}g\left(2\right)=2.$ If there exists atleast one $cϵ(0,2)$ such that $f^{\prime }\left(c\right)=k{g}^{\prime }\left(c\right)$, then $k$ must be

1. 2
2. 3
3. $\frac{1}{2}$
4. 1