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**Desperate** on
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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) on [a,b], inclusive. USE THE EXTREME VALUE THEOREM AS A LEMMA (A PRELIMINARY RESULT) TO PROVE THE IMAGE THEOREM.