Elements of the Differential Calculus
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Similarly for the other critical values of Ex. 6.
83. Conditions for maxima and minima derived from Tay- lor's theorem.
In this article, as in the preceding, the function and its derivatives are supposed to be continuous in the vicinity of x = a; otherwise the method of Art. 81 must be used.
Let ^(«) be a maximum value of ^(x); then it follows from the definition that ^(a) is greater than either of the neighboring values, (^(a + A), 0(a — 7i), when A is taken small enough. Hence(^a + h') — (a) and (j)Qa — h')—
140 DIFFERENTIAL CALCULUS [Ch. VI.
Let (p(x + h'), (^(x—K) be expanded in powers of A by Taylor's theorem ; then 4>(x + li) = ^(x-)+'(a^ will be numerically larger than the sum of the remaining terms in the second member of either of the last two equa- tions.
What to read after Elements of the Differential Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Mcmahon James to read online
To quickly assess the difficulty of the text, read a short excerpt:
Similarly for the other critical values of Ex. 6.
83. Conditions for maxima and minima derived from Tay- lor's theorem.
In this article, as in the preceding, the function and its derivatives are supposed to be continuous in the vicinity of x = a; otherwise the method of Art. 81 must be used.
Let ^(«) be a maximum value of ^(x); then it follows from the definition that ^(a) is greater than either of the neighboring values, (^(a + A), 0(a — 7i), when A is taken small enough. Hence
140 DIFFERENTIAL CALCULUS [Ch. VI.
Let (p(x + h'), (^(x—K) be expanded in powers of A by Taylor's theorem ; then 4>(x + li) = ^(x-)+'(a^ will be numerically larger than the sum of the remaining terms in the second member of either of the last two equa- tions.
What to read after Elements of the Differential Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Mcmahon James to read online
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