{"paper":{"title":"Recognizing difference quotients of real functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jimmy Yau, Trevor Richards","submitted_at":"2017-05-23T03:47:16Z","abstract_excerpt":"For a real function $f:[0,1]\\to\\mathbb{R}$, the difference quotient of $f$ is the function of two real variables $\\operatorname{DQ}_f(a,b)=\\dfrac{f(b)-f(a)}{b-a}$, which we view as defined on the triangle $\\mathcal{T}=\\{(a,b):0\\leq a<b\\leq1\\}$. In this paper we investigate how to determine whether a given function of two variables $H(a,b)$ is the difference quotient of some real function $f(x)$. We develop three independent methods for recognizing such a function $H$ as a difference quotient, and corresponding methods for recovering the underlying function $f$ from $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02351","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}