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Calculus  behaviour of functions  first derivative and the likes 
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#1
Nov109, 04:20 AM

P: 80

1. The problem statement, all variables and given/known data
Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P'(x) = 0. If P(–1) < P(1), then in the interval [–1, 1] (1) P(–1) is not minimum but P(1) is the maximum of P (2) P(–1) is minimum but P(1) is not the maximum of P (3) Neither P(–1) is the minimum nor P(1) is the maximum of P (4) P(–1) is the minimum and P(1) is the maximum of P 2. Relevant equations The answer is 1. 3. The attempt at a solution
Now P(–1) < P(1) ⇒ P(–1) cannot be minimum in [–1, 1] as minima in this interval is at x = 0.  xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  The question is solved. That is not the problem. What I am wondering about right now is that such a logical question is too precious to be let go of without a discussion. Do you have any comments regarding either the geometrical interpretation or logical deduction of the answer? For me, the questions are getting monotonous by the day and I have almost lost the thrill of learning because now the questions are just too clear. However, I am sure you will have a lot to discuss about it, right? 


#2
Nov109, 04:24 AM

P: 80

If anyone of you is a teacher  you must have had some sort of a frustrating experience on how the crystal clear logic doesn't even appeal to the students.



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