See the explanation section below.<\/p>\n
A point of inflection is a point on the graph at which the concavity of the graph changes.<\/p>\n
If a function is undefined at some value of ##x##, there can be no inflection point.<\/p>\n
However, concavity can change as we pass, left to right across an ##x## values for which the function is undefined.<\/p>\n
Example<\/b><\/p>\n
##f(x) = 1\/x## is concave down for ##x < 0## and concave up for ##x > 0##.<\/p>\n
The concavity changes “at” ##x=0##.<\/p>\n
But, since ##f(0)## is undefined, there is no inflection point for the graph of this function.<\/p>\n
graph{1\/x [-10.6, 11.9, -5.985, 5.265]} <\/p>\n
Example 2<\/b><\/p>\n
##f(x) = root3x## is concave up for ##x < 0## and concave down for ##x > 0##.<\/p>\n
##f'(x) =1\/(3root3x^2)## and ##f'(x) =(-2)\/(9root3x^5)##<\/p>\n
The second derivative is undefined at ##x=0##.<\/p>\n
But, since ##f(0)## is defined, there is an inflection point for the graph of this function. Namely, ##(0,0)##<\/p>\n
graph{x^(1\/3) [-3.735, 5.034, -2.55, 1.835]} <\/p>\n","protected":false},"excerpt":{"rendered":"
See the explanation section below. A point of inflection is a point on the graph at which the concavity of the graph changes. If a function is undefined at some value of ##x##, there can be no inflection point. However, Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-72023","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/72023","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=72023"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/72023\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=72023"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=72023"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=72023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}