On the mean value theorem

By Jingcheng Tong. 2000

81 citations recorded by the source corpus.

sin θ If F has a max or min at some c ∈ (a, b), then F (c) = 0 and f (c) = f(b)−f(a) b−a as desired. In fact, I claim that F must have a max or min in (a, b). Because otherwise, both the max and min must occur at a or b. As F (a) = F (b) = 0 this forces both the max and min to be 0 and F (x) to be identically 0. In this case, every x ∈ (a, b) is a max and a min, contradicting the hypothesis that F has no max or min in (a, b).

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d172955efdb40a9942d38eb132197774a6686ef

Citations in the corpus

• Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, unknown): “Recent work of Kozlov [25] and Sorokin [35] provides some slight improvement in these results for the special case K = Q( √ −1), although their estimates are constrained to possess the same salient features.”