{"id":5668,"date":"2021-09-27T19:43:59","date_gmt":"2021-09-27T14:13:59","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5668"},"modified":"2021-11-13T17:31:07","modified_gmt":"2021-11-13T12:01:07","slug":"maxima-and-minima-class-12","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/maxima-and-minima-class-12\/","title":{"rendered":"Maxima and Minima Class 12"},"content":{"rendered":"

Here you will learn definitions and concepts of local and absolute maxima and minima class 12.<\/p>\n

Let’s begin –<\/p>\n

Maxima and Minima Class 12<\/h2>\n

Local Maxima<\/strong> <\/h4>\n

A function f(x) is said to have local maxima at x = a if there exist a neighbourhood (a – h, a + h) – {a} such that <\/p>\n

f(a) > f(x) for all x \\(\\in\\) (a – h, a + h) – {a}<\/p>\n

Local Minima<\/strong> <\/h4>\n

A function f(x) is said to have local minima at x = a if there exist a neighbourhood (a – h, a + h) – {a} such that <\/p>\n

f(a) < f(x) for all x \\(\\in\\) (a – h, a + h) – {a}<\/p>\n

Absolute Maxima (Global Maxima)<\/strong><\/h4>\n

A function f has an absolute maxima (or global maxima) at c if f(c) \\(\\ge\\) f(x) for all x in D, where D is the domain of f. The number f(c) is called the maximum value of on D.<\/p>\n

Absolute Minima (Global Minima)<\/strong><\/h4>\n

A function f has an absolute minima (or global minima) at c if f(c) \\(\\le\\) f(x) for all x in D and the number f(c) is called the minimum value of on D. The maximum and minimum values of f are called the extreme values of f.<\/p>\n

Note :<\/strong><\/p>\n

(i) the maximum & minima values of a function are also known as local\/relative maxima or local\/relative minima as these are greatest & least values of the function relative to some neighbourhood of the point in question.<\/p>\n

(ii) the term ‘extrema’ is used both for maxima or minima.<\/p>\n

(iii) a maximum (minimum) value of a function may not be the greatest (least) value in a finite interval.<\/p>\n

(iv) a function can have several extreme values & a local minimum value may even be greater than a local maximum value.<\/p>\n

(v) local maximum & local minimum values of a continuous function occur alternatively & between two consecutives local maximum values there is a local minimum value &  vice versa.<\/p>\n\n\n

\n
Next – First Derivative Test for Maxima and Minima<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Monotonic Function \u2013 Definition and Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn definitions and concepts of local and absolute maxima and minima class 12. Let’s begin – Maxima and Minima Class 12 Local Maxima  A function f(x) is said to have local maxima at x = a if there exist a neighbourhood (a – h, a + h) – {a} such that  f(a) …<\/p>\n

Maxima and Minima Class 12<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[37],"tags":[76,83,79,82,84],"yoast_head":"\nMaxima and Minima Class 12 - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn definitions and concepts of local and absolute maxima and minima class 12.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/maxima-and-minima-class-12\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Maxima and Minima Class 12 - 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