Question: let f be a smooth (possibly nonlinear) function. The first derivative test tells us that if f achieves a local max (among points in )

let f be a smooth (possibly nonlinear) function. The first derivative test tells us that if f achieves a local max (among points in ) at some x then f(x)d 0 whenever d is a feasible direction at x. Suppose that among the inequalities defining , the first k of them are equalities at x and the remaining mk of them are not. Explain why the feasible directions at x are precisely the vectors d such that P n j=1 aijdj 0 for i = 1, . . . , k

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