Continuity and intermediate value theorem

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SUMMARY

The discussion centers on the application of the Intermediate Value Theorem to the function f(x) = x^3 - 12x^2 + 44x - 46 over the interval [1, 7]. The calculated values at specific points reveal that f(1) = -13, f(2) = 2, f(4) = 2, f(5) = -1, and f(6) = 2. The correct intervals where the function changes sign, indicating the presence of roots, are (1, 2), (4, 5), and (5, 6). However, the initial answer was not accepted, suggesting a potential issue with the formatting of the response rather than the mathematical reasoning.

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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
 

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