{"id":32,"date":"2012-08-07T06:38:30","date_gmt":"2012-08-07T06:38:30","guid":{"rendered":"http:\/\/softwareeveryday.wordpress.com\/?p=32"},"modified":"2012-08-07T06:38:30","modified_gmt":"2012-08-07T06:38:30","slug":"function-minima-and-maxima-recap","status":"publish","type":"post","link":"https:\/\/www.softwareeverydayblog.com\/?p=32","title":{"rendered":"Function minima and maxima recap."},"content":{"rendered":"

Came accross interesting problem in some GATE computer science paper.<\/p>\n

Consider the function f(x) = sin (x) in the interval x \u2208 [\u03c0\/4, 7\u03c0\/4]. The number and location(s) of
\nthe local minima of this function are
\n(A) One, at \u03c0\/2
\n(B) One, at 3\u03c0\/2
\n(C) Two, at \u03c0\/2 and 3\u03c0\/2
\n(D) Two, at \u03c0\/4 and 3\u03c0\/2<\/p>\n

Was quick to answer (B).\u00a0Here is the plot of the graph, one of the minima is clearly\u00a03\u03c0\/2. However, in this case\u00a0\u03c0\/4 is a local minimum too (definitely\u00a0clearer if we draw the function just within the ranges). So the answer is (D).<\/strong><\/p>\n

\"\"<\/a><\/p>\n

Note that this is only true when the interval is closed i.e. including points\u00a0\u03c0\/4 and 7\u03c0\/4. If the problem was\u00a0x \u2208 (\u03c0\/4, 7\u03c0\/4) then\u00a0\u03c0\/4 is NOT a local minima as its NOT part of the function domain. Also, no matter what point we pick close to \u03c0\/4 as our local minimum there will be a number lower than that.\u00a0In that case this function would have just one minimum at\u00a03\u03c0\/2.<\/p>\n","protected":false},"excerpt":{"rendered":"

Came accross interesting problem in some GATE computer science paper. Consider the function f(x) = sin (x) in the interval x \u2208 [\u03c0\/4, 7\u03c0\/4]. The number and location(s) of the local minima of this function are (A) One, at \u03c0\/2 (B) One, at 3\u03c0\/2 (C) Two, at \u03c0\/2 and 3\u03c0\/2 (D) Two, at \u03c0\/4 and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/posts\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32"}],"version-history":[{"count":1,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":200,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=\/wp\/v2\/posts\/32\/revisions\/200"}],"wp:attachment":[{"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.softwareeverydayblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}