If   and   are differentiable functions in   such that  , then there exists   such that

$\text{ Let }F\left(x\right)=f\left(x\right)-2g\left(x\right), F\left(0\right)=f\left(0\right)-2g\left(0\right)=2, F\left(1\right)=f\left(1\right)-2g\left(1\right)=2$ 
 F(x) satisfies the conditions for Rolle’s theorem and there exist c, such that 
$F^{\mathrm{\prime }}\left(c\right)=0\text{ or }{f}^{\mathrm{\prime }}\left(c\right)-2g^{\mathrm{\prime }}\left(c\right)=0\text{ for }0<c<1$