An Elementary Treatise On the Differential Calculus, Containing the Theory of Plane Curves, With Numerous Examples
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On the Differential Calculus, Containing the Theory of Plane Curves, With Numerous Examples Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On the Differential Calculus, Containing the Theory of Plane Curves, With Numerous Examples
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For students who are unacquainted with this form of the Theorem, it may be observed that the conditions for a maximum or minimum can be readily established from the form of Taylor's Series given in Art. 54, viz., h 2 h 3 f(a + h) -/(«) = hf(a) + —f\a) + /"» + &c. ; 1.2 1.2.3 for when h is very small and the coefficients/^),/" (a), &c. finite, it is evident that the sign of the series at the right-hand side depends on that of its first term, and hence all the results arrived at in the above and ...the subsequent Articles can be readily established.
Condition for a Maximum or a Minimum.
171 But the expressions at the left-hand side in these equations are both positive for small values of h when/"(#) is positive ; and negative, when f\a) is negative ; therefore f(a) is a maximum or a minimum according as f\a) is negative or positive.
If, however, f'(a) vanish along with f(a), we have, by Art. 75, f(a + h) -/(«) =_!_/'» + -_£_/*(* + Oh), f{a - h) -fid) = -if'W + *; /*(
What to read after An Elementary Treatise On the Differential Calculus, Containing the Theory of Plane Curves, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Williamson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
For students who are unacquainted with this form of the Theorem, it may be observed that the conditions for a maximum or minimum can be readily established from the form of Taylor's Series given in Art. 54, viz., h 2 h 3 f(a + h) -/(«) = hf(a) + —f\a) + /"» + &c. ; 1.2 1.2.3 for when h is very small and the coefficients/^),/" (a), &c. finite, it is evident that the sign of the series at the right-hand side depends on that of its first term, and hence all the results arrived at in the above and ...the subsequent Articles can be readily established.
Condition for a Maximum or a Minimum.
171 But the expressions at the left-hand side in these equations are both positive for small values of h when/"(#) is positive ; and negative, when f\a) is negative ; therefore f(a) is a maximum or a minimum according as f\a) is negative or positive.
If, however, f'(a) vanish along with f(a), we have, by Art. 75, f(a + h) -/(«) =_!_/'» + -_£_/*(* + Oh), f{a - h) -fid) = -if'W + *; /*(
What to read after An Elementary Treatise On the Differential Calculus, Containing the Theory of Plane Curves, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Williamson to read onlineMoreLess
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