(1) The Mean Value Theorem states: Let f be continuous over the closed [a, b] and...

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(1) The Mean Value Theorem states: Let f be continuous over the closed [a, b] and differentiable over the open interval (a, b). Then, there exists at least one point c E (a, b) such that: f(b) - f(a) f'(c) = Provide the TL;DR version of the MVT: b-a (2) AITA for Arguing in Recitation???!!! Some girl (18ishF) was working with my (M, 2nd time taking the course) table group as we were trying to find the local extrema of some function. Well, I know we went over that skill last Monday in class (I don't even know if she was there that day) and so I said we could use the Second Derivative Test. But this girl insisted that the First Derivative Test was the correct approach. This disagreement escalated quickly to both of us being pretty defensive and not willing to budge. Well, she suggested we try both methods and I told her that I didn't need her permission to try the method I was already going to try anyway. You could say things got pretty tense after that, even our TA was avoiding our side of the room. AITA for not being more open-minded about other potential strategies or was I right to stick to my guns??? Student is writing a response... (1) The Mean Value Theorem states: Let f be continuous over the closed [a, b] and differentiable over the open interval (a, b). Then, there exists at least one point c E (a, b) such that: f(b) - f(a) f'(c) = Provide the TL;DR version of the MVT: b-a (2) AITA for Arguing in Recitation???!!! Some girl (18ishF) was working with my (M, 2nd time taking the course) table group as we were trying to find the local extrema of some function. Well, I know we went over that skill last Monday in class (I don't even know if she was there that day) and so I said we could use the Second Derivative Test. But this girl insisted that the First Derivative Test was the correct approach. This disagreement escalated quickly to both of us being pretty defensive and not willing to budge. Well, she suggested we try both methods and I told her that I didn't need her permission to try the method I was already going to try anyway. You could say things got pretty tense after that, even our TA was avoiding our side of the room. AITA for not being more open-minded about other potential strategies or was I right to stick to my guns??? Student is writing a response...