Essential Knowledge 1.2B1

Essential Knowledge 1.2B1 Students will know that continuity is an essential condition for theorems such as the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem.

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The Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem only work over continuous intervals. That's about all there is to say. It's why we studied continuity.