Συνεπειες Θ.Μ.Τ.

Εστω συναρτηση f:\mathbb{R}\rightarrow \mathbb{R} , τρεις φορες παραγωγισιμη.

Ισχυει: 2f(x)=x(1+f'(x)),\forall x \in \mathbb{R}

Να δειξετε οτι:

α) η f'' ειναι σταθερη.

β) αν f'(1)=3, τοτε f(x)=x^2+x , x\in \mathbb{R}.

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