Calculus Want to read a paragraph at "Calculus", by R. A. Adams, 8th or 7th ed.

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The discussion centers on a request for an updated translation of the first paragraph from Chapter 4.2, titled "Test of the First Derivative," in the Spanish 6th edition of "Cálculo" by Robert A. Adams. The original text explains that most functions in elementary calculus have nonzero derivatives across their domains, except at a limited number of critical points, singular points, and endpoints. It emphasizes that on intervals between these points, the derivative is non-zero, indicating whether the function is increasing or decreasing. Additionally, it states that if a function is continuous and increases to the left of a point and decreases to the right, it must have a local maximum at that point. The participant expresses a preference for the English 9th edition and plans to purchase it in the future for better comprehension.
mcastillo356
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Hi,PF

I've got "Cálculo", Spanish 6th edition, by Robert A. Adams. At Chapter 4.2, would like to read an updated (guess it might be better) 1st. paragraph of the section I translate "Test of the first derivate".

Regards
 
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Most functions you will encounter in elementary calculus have nonzero derivatives ev- erywhere on their domains except possibly at a finite number of critical points, singular points, and endpoints of their domains. On intervals between these points the derivative exists and is not zero, so the function is either increasing or decreasing there. If f is continuous and increases to the left of x0 and decreases to the right, then it must have a local maximum value at x0. The following theorem collects several results of this type together.

9th english edition
 
Thanks! Willing to buy it, don't know when. I manage better in English!
 

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