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solve by using Find the shortest distance from the point (1,-1,1) to the surface

ID: 3372554 • Letter: S

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Find the shortest distance from the point (1,-1,1) to the surface z = xy. Set up the squared distance as a function of x, y, find the critical points of the function, and test them by Theorem IX. Suppose that F(x, y) is defined and differentiable throughout a region R of which (a, b) is an interior point, and suppose that the first partial derivatives of F vanish at that point. Suppose further that the partial derivatives F, and F2 are differentiable at (a, b). Let us write A = F11(a, b), B - Fl2(a, b), C = F22(a, b). Then If B2 - AC 0, F has a relative minimum at (a, b); If B2- AC

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