We have been finding a set of optimal parameters for the linear least-squares regression minimization problem by identifying critical points, i. e. points at which the gradient of a # function is the zero vector, of the following function: F(Qo, ... ,Qm) = EN=1(Q, + Q7Xnı + ... + QmXnM - yn)?.
Please help to justify this methodology in the following way. Letting G: Rd - R be any function that is differentiable everywhere, show that, if G has a local minimum at a EB point xo, then its gradient is the zero vector there, i. e., VG(X) = 0.