8. Let $\alpha$ Î R. Prove that a function $\mathrm { f } : \mathrm { R } - - > \mathrm { R }$ is differentiable at $\alpha$ if and only if there is a function $\mathrm { g } : \mathrm { R }$ --> $R$ which is continuous at $\alpha$ and satisfies $f ( x ) - f ( \alpha ) = f ( x ) ( x - \alpha )$ for all $x \hat { I } R$.\\