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Unformatted text preview: time of day on both days? Why or why not. Solution. This one is fun to do, so I wont give the full solution. A hint is to consider the following functions f ( x ) = The monks altitude at time x on day 1 , g ( x ) = The monks altitude at time x on day 2 Then f and g are continuous functions on the interval [7 am , 7 pm]. We want to show that f ( x ) = g ( x ) for some x in [7 am , 7 pm]. Equivalently, we want to show that f ( x )-g ( x ) = 0. Now consider the value of f ( x )-g ( x ) for x = 7 am and x = 7 pm and see what you get. 4. Prove that the polynomial x 3 + 2 x 2-5 x + 1 has at least three zeros. (Hint: consider f (-4), f (0), f (1) and f (2).) Solution. Use the hint. That is, compute f (-4), f (0), f (1) and f (2) and see what you get. 5. (Challenge problem) Show that at any given time there are two diametrically opposite points on the globe that have the same temperature. 1...
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09
- Intermediate Value Theorem