Intermediate Value Theorem 1. What must you prove in order to invoke the Intermediate Value Theorem? 2. Draw a picture illustrating the Intermediate Value Theorem. 3. Let 𝑣 𝑡 represent the velocity of an object moving along the 𝑥 -­‐axis, and be continuous everywhere. For 0 < 𝑡 < 40, must there be a time when 𝑣 𝑡 = −15? Justify your answer. 𝑡 (sec) 0 10 20 30 40 𝑣(𝑡) (m/sec) -­‐20 -­‐30 -­‐20 -­‐10 0 

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