The Image Theorem: The image theorem, a corollary of the intermediate value theorem
Chapter 2, Problem 14(choose chapter or problem)
The Image Theorem: The image theorem, a corollary of the intermediate value theorem, expresses the property that if f is continuous on the interval [a, b], then the image (the set of y-values) of f on [a, b] is all real numbers between the minimum of f(x) and the maximum of f(x) on [a, b], inclusive. Use the extreme value theorem as a lemma (a preliminary result) to prove the image theorem.
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