The purpose of approximation is finding optimal point x∗ i.e. ∇F(x∗)=0. We need a step/search direction Δx and step size t. Taylor approximation has polynomial arguments that is a step and parameters of derivatives at the start point. The first degree of Taylor approximation has one adding term from start point (x0,F(x0)). The adding term ∇F(x)Δx is consistent with a parameter (gradient ∇F(x)) and a argument (step Δx).