Continuity and intermediate value theorem

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The function f(x) = x^3 - 12x^2 + 44x - 46 is evaluated at several points between x = 1 and x = 7, yielding values that suggest the function crosses the x-axis in the intervals (1,2), (4,5), and (5,6). Despite this, the proposed answer was not accepted, leading to speculation about potential formatting issues with the response. The graph of the function visually supports the identified intervals as valid solutions. The discussion highlights the importance of both analytical and graphical methods in confirming the application of the Intermediate Value Theorem. Proper formatting may be crucial for acceptance in such evaluations.
dramadeur
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f(x) = x^3 - 12x^2 + 44x - 46

GanLOBR.png

x from 1 to 7

The attempt at a solution:
f(1) = -13
f(2) = 2
f(4) = 2
f(5) = -1
f(6) = 2
So naturally, the answer should be: (1,2) U (4,5) U (5,6)
right? Well, it didn't accept this answer. I think there is something wrong with whatever that is accepting the answer... because it seems to be the correct one.
Even by looking at the graph of the function you'd tell these are the only intervals fitting the criteria...
3KpSros.png

 
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Maybe it is the way you have formatted your answer.

AM
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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