Suppose that f: R → R is a continuous function. Show that there exists a point on the graph of f that is closest to the origin. (Hint: Let d(x) = √√x² + f(x)² be the distance of the point (x, f(x)) on the graph to the origin and prove that this function has a minimum on the interval [-a, a] where a = |ƒ(0)|.)

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