{"created":"2021-03-01T05:58:50.175992+00:00","id":6402,"links":{},"metadata":{"_buckets":{"deposit":"c0053438-a0cb-419e-adda-52a7fc5cd2cf"},"_deposit":{"id":"6402","owners":[],"pid":{"revision_id":0,"type":"depid","value":"6402"},"status":"published"},"_oai":{"id":"oai:kitami-it.repo.nii.ac.jp:00006402"},"item_2_biblio_info_6":{"attribute_name":"\u66f8\u8a8c\u60c5\u5831","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1976-06","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"443","bibliographicPageStart":"441","bibliographicVolumeNumber":"7","bibliographic_titles":[{"bibliographic_title":"\u5317\u898b\u5de5\u696d\u5927\u5b66\u7814\u7a76\u5831\u544a"}]}]},"item_2_description_14":{"attribute_name":"\u30d5\u30a9\u30fc\u30de\u30c3\u30c8","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_description_4":{"attribute_name":"\u6284\u9332","attribute_value_mlt":[{"subitem_description":"Let f\uff08x\uff09 be differentiable, \u03b1\uff1cx\uff1c\u03b2\uff0e We putr(x, y) = { (f(x)?f(y))/(x?y), x\u2260y, f\u00b4(x),\u3000         \uff58\uff1d\uff59\u3000\u3000        \uff081\uff09We have the following :(i)\u3000 r(x, y)\uff1dr(y, x),(ii)  r(x, z)(x?z)\uff1dr(x, y)(x?y)\uff0br(y, z)(y?z),(iii)\u3000<lim>___x\u2192y r(x, y)\uff1dr(y, y),(iv)\u3000r is continuous at a point (x, y) of x\u2260y. Newly, having no relation to (1), let r(x, y) be a real function of 2-varia-bles, \u03b1\uff1cx, y\uff1c\u03b2. In \uff3b1\uff3d, if r(x, y) satisfies the previous (i), (ii), (iii), (iv), then we obtain Rolle\u2019s theorem and mean value theorem, namely, (v)  if r(a, b)\uff1d0\uff0ca\uff1cb, then there exists c(a\uff1cc\uff1cb) such that\u3000r(c, c)\uff1d0\uff0c(vi)\u3000fo\uff52 \uff41,\uff42(a\uff1cb), there exists c(a\uff1cc\uff1cb) such that r(a, b)\uff1dr(c, c).The purpose of this note is to point out that if r(x, y) satisfies (i), (ii), (iii), then we have (iv), (v), (vi) and Cauchy's theorem, namely,(vii)\u3000if a function s(x, y) satisfies (i), (ii), (iii) and s(x, y)\u22600, (a\u2266x, y\u2266b)\u3000\u3000\u3000for a\uff1cb, then there exists c(a\uff1cc\uff1cb) such that (r(a, b))/(s(a, b)) = (r(c, c))/(s(c, c)).","subitem_description_type":"Abstract"}]},"item_2_publisher_32":{"attribute_name":"\u51fa\u7248\u8005","attribute_value_mlt":[{"subitem_publisher":"\u5317\u898b\u5de5\u696d\u5927\u5b66"}]},"item_2_select_15":{"attribute_name":"\u8457\u8005\u7248\u30d5\u30e9\u30b0","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_creator":{"attribute_name":"\u8457\u8005","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"ISOBE, Kiro"}],"nameIdentifiers":[{"nameIdentifier":"32464","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"\u30d5\u30a1\u30a4\u30eb\u60c5\u5831","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-11-22"}],"displaytype":"detail","filename":"7-2-13.pdf","filesize":[{"value":"1.1 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"7-2-13.pdf","url":"https://kitami-it.repo.nii.ac.jp/record/6402/files/7-2-13.pdf"},"version_id":"574cb933-32b0-4005-9fa3-837a923accb3"}]},"item_language":{"attribute_name":"\u8a00\u8a9e","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"\u8cc7\u6e90\u30bf\u30a4\u30d7","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A Certain Consideration on Derivatives and Rolle's Theorem","item_titles":{"attribute_name":"\u30bf\u30a4\u30c8\u30eb","attribute_value_mlt":[{"subitem_title":"A Certain Consideration on Derivatives and Rolle's Theorem"}]},"item_type_id":"2","owner":"1","path":["7/15/23"],"pubdate":{"attribute_name":"\u516c\u958b\u65e5","attribute_value":"2007-04-09"},"publish_date":"2007-04-09","publish_status":"0","recid":"6402","relation_version_is_last":true,"title":["A Certain Consideration on Derivatives and Rolle's Theorem"],"weko_creator_id":"1","weko_shared_id":3},"updated":"2021-03-01T06:53:11.056631+00:00"}