Let $X$ be a Banach space, we define

$ \phi\_-(y)=\lim\_{t\rightarrow{0^+}}=\frac{|x|-|x-ty|}{t} $  

$\phi\_+(y)=\lim\_{t\rightarrow{0^+}}=\frac{|x+ty|-|x|}{t} $

Then $ M^\*(x)= \{ x\* \in X^\*: \phi\_-(y)\leq x^\*(y) \leq \phi\_+(y) \}=\{x^\* \in X^\*: |x^\*|=1 \ and \ x\*(x)=|x|\}.$

I don't know how to prove the last equality.