{
  "id": "1706.02351",
  "version": "v1",
  "published": "2017-05-23T03:47:16.000Z",
  "updated": "2017-05-23T03:47:16.000Z",
  "title": "Recognizing difference quotients of real functions",
  "authors": [
    "Trevor Richards",
    "Jimmy Yau"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "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 $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-23T03:47:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real function",
      "recognizing difference quotients",
      "real variables",
      "independent methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}