Submanifold in $R^n$ with positive sectional curvature

Question

I’m trying to prove that for a compact hypersurface $M⊂R^n$($n>2$),there exists a point p where $sec(σ)>0$ for all 2-planes $σ ⊂T_pM$. My idea is : Since M is compact, we can choose a maximal point p of distance function $r(x)=d(0,x)$ on $M$ and try to show $sec_p>0$. By Gauss equation, it suffices to show the 2nd fundamental form is positive definite at p, and I only know that 2nd fundamental form equals to Hess$r$ when the hypersurface $⊂r^{-1}(a)$. But how can Hessian make sense here? Is there any other method to deal with it? Thanks in advance.