Question: 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:

Help to justify this methodology in the following way. Letting be any

function that is differentiable everywhere, show that, if has a local minimum at a

point , then its gradient is the zero vector there, i.e., .

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