Sentence in English in textbook "Calculus", by Robert A. Adams

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mcastillo356
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Hi, PF

I've got a translation into spanish of the sixth edition of "Calculus", by Robert A. Adams. At the second chapter, "Differentiation", eleventh section, I would like to know: the title of the section (Could it be "Velocity and Acceleration"?); and a sentence of the Example 2 ("A point P moves along the x axis..."): at the solution of the question (d), I have something like "Velocity is continous for all t, so, according to the Mean value theorem...". Wich would be the sentence in English?

Thanks!
 

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The velocity is continuous for all t so, by the Intermediate-Value Theorem, has a constant sign on the intervals between the points where it is 0.
 
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mcastillo356
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In my edition, it mentioned Mean Value Theorem, and it didn't make sense.

Greetings!
 
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Yeah, it's probably easy to mix up 'Teorema del valor medio' and 'Teorema del valor intermedio'.
 
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The English word "mean" refers to an average, so the mean value theorem talks about the average value.
 
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mathwonk
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actually every derivative, continuous or not, has the intermediate value property, and the proof uses the mean value theorem, or at least its equivalent version, rolle's theorem. ( a function that goes up and then down, must take the same value twice and hence must level off somewhere in between.) so many interpretations are possible.
 
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