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

• Calculus
Gold Member
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!

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.

• mcastillo356
Gold Member
In my edition, it mentioned Mean Value Theorem, and it didn't make sense.

Greetings!

Yeah, it's probably easy to mix up 'Teorema del valor medio' and 'Teorema del valor intermedio'.

• PeroK and mcastillo356
The English word "mean" refers to an average, so the mean value theorem talks about the average value.

• mcastillo356
mathwonk
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