Paper 1, Section II, D

Analysis I | Part IA, 2009

State and prove the intermediate value theorem.

Let f:RRf: \mathbb{R} \rightarrow \mathbb{R} be a continuous function and let P=(a,b)P=(a, b) be a point of the plane R2\mathbb{R}^{2}. Show that the set of distances from points (x,f(x))(x, f(x)) on the graph of ff to the point PP is an interval [A,)[A, \infty) for some value A0A \geqslant 0.

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