{"id":5891,"date":"2025-08-11T10:13:16","date_gmt":"2025-08-11T04:43:16","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5891"},"modified":"2025-08-11T10:13:16","modified_gmt":"2025-08-11T04:43:16","slug":"relationship-between-differentiability-and-continuity","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/calculus-and-differeential-equations\/relationship-between-differentiability-and-continuity","title":{"rendered":"Relationship between Differentiability and Continuity"},"content":{"rendered":"<h2 style=\"text-align: justify;\">Theorem:<\/h2>\n<p style=\"text-align: justify;\">If a function is differentiable at any point, then it is necessarily continuous at that point; proof of this theorem follows from definitions of differentiability and continuity.<\/p>\n<p style=\"text-align: justify;\"><strong>Note:<\/strong> The converse of this theorem is not true.<\/p>\n<p style=\"text-align: justify;\">i.e., continuity is a necessary but not a sufficient condition for the existence of a finite derivative (differentiability).<\/p>\n<p>i.e., differentiability \u21d2 continuity<\/p>\n<p>But continuity \u21cf differentiability<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Theorem: If a function is differentiable at any point, then it is necessarily continuous at that point; proof of this<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1733,5],"tags":[1739,1738],"class_list":["post-5891","post","type-post","status-publish","format-standard","hentry","category-calculus-and-differeential-equations","category-ee","tag-continuity","tag-differentiability"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=5891"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5891\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}