In this talk, we will discuss local polynomial convexity of a smooth $n$-dimensional manifold $M$ embedded in $\mathbb{C}^n$. If $T_pM \subset T_p\mathbb{C}^n$ is a totally real subspace, then $M$ is locally polynomially convex at $p$. For a generic embedding $M^n \subset \mathbb{C}^n$, we are interested in assessing polynomial convexity of $M$ at a CR-singularity, i.e., at a point where $T_pM$ is not totally real. An order one CR-singularity in $M$ can be broadly classified as elliptic or hyperbolic. It is known that elliptic points give obstruction to polynomial convexity. For dimension two, $M^2 \subset \mathbb{C}^2$ is locally polynomially convex at a hyperbolic complex point. We will investigate local polynomial convexity of $M^n \subset \mathbb{C}^n$ at hyperbolic points in higher dimension.