Question: Consider the curve y = x2 2 in the Cartesian plane. Let D be the distance from a point (x, y) on the curve to

Consider the curve y = x2 2 in the Cartesian plane. Let D be the distance from a point (x, y) on the curve to the origin. The value of D is minimised when S = D2 is minimised. a) Show that S = x4 3x2 + 4. (3 marks) b) Find the critical value(s) of S. (4 marks) c) Determine the nature of the critical value(s) of S using the Second Derivative Test. (4 marks) d) What are the coordinates of the point(s) on the curve that are closest to the origin, and what is this minimum distance? (4 marks) Marks

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