Prove that if g is strictly concave and twice

Question

Let (S, d) ∈ F be a bargaining game. Denote by x₂ = g(x₁) the equation defining the north-east boundary of S.

Prove that if g is strictly concave and twice differentiable, then the point x∗ = N (S, d) is the only efficient point x in S satisfying -g" (x₁)(x₁ - d₁) = (x₂ - d₂).