consider Nonlinear Optimization problem below

Let g be a twice continuously differentiable, positive function of n variables. Show that a vector x satisfying: . g(x) c+ Vg(x) =0, and . g(x) V2g(x) - Vg(x) Vg(x) is positive definite, must be an unconstrained strong local minimizer of c x + logg(x)