{"id":7907,"date":"2022-05-16T15:23:23","date_gmt":"2022-05-16T09:53:23","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7907"},"modified":"2025-06-02T20:45:24","modified_gmt":"2025-06-02T15:15:24","slug":"what-are-the-increasing-and-decreasing-functions","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-the-increasing-and-decreasing-functions\/","title":{"rendered":"What are the Increasing and decreasing functions?"},"content":{"rendered":"\n<p>Introduction(<a href=\"https:\/\/www.mathsisfun.com\/sets\/functions-increasing.html\" target=\"_blank\" rel=\"noreferrer noopener\">Increasing and decreasing functions<\/a>)- A function is said to be increasing function in an interval [a, b] if y increases as well as x increases from a to b.<\/p>\n\n\n\n<p>Or in other words, A function is said to be an increasing function in [a, b] if its first derivative is greater than zero for all values of x in an interval [a, b].<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/RFyYp2HF1C-gzknBko8rtAkQ5dnfhtHwHvddZKKetxCmiH22kDdKjYX4MQ0h2UJJRgdfha9K9X1dt26fZ3dOz66LEuHOurrrUiIeY4S3foaHFqVlJ5Ym-6skswp-fo-mAVL4QGSJvVkabFfo2A\" alt=\"\"\/><\/figure>\n\n\n\n<p>And<\/p>\n\n\n\n<p>A function is said to be decreasing function in an interval [a, b] if y decreases as well as x increases from a to b.<\/p>\n\n\n\n<p>\u201cIf the first derivative is less than zero for all values of x in an interval [a, b] then the function y = f(x) is a decreasing function in [a, b].<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/FrNfN7qUKnVlBpKaSi7ceTbk6TZLyLQU0grASYKVFujr4ck5YsrajoFfpv3YCmvYlM-EYaqc4VXAXOo7ephuHx_v784vye3vcEoZ5iwNdvAepd9xldqPQkKV4_bOzod-yISrdB4YfbNvCb365A\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Maximum and minimum<\/strong>(Increasing and decreasing functions)<\/h2>\n\n\n\n<p>We call a function f(x) is maximum at x = a. If f(a) is greater than every other value of f(x) in the immediate neighbourhood of x = a. Then (i.e., f(x) ceases to increase but begins to increase at x = a. <\/p>\n\n\n\n<p>Similarly, the minimum value of f(x) will be that value at x = b which is less than other values in the immediate neighbourhood of x = b.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Maxima and minima of function of two variables<\/strong><\/h2>\n\n\n\n<p>As we know that the value of a function at maximum point is the maximum value of a function. <\/p>\n\n\n\n<p>Similarly, the value of a function at minimum point is the minimum value of a function.<\/p>\n\n\n\n<p>The maxima and minima of a function is an extreme biggest and extreme smallest point of a function in a given range (interval) or entire region. <\/p>\n\n\n\n<p>Pierre de Fermat was the first mathematician to discover general method for calculating maxima and minima of a function. The maxima and minima are complement of each other.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Maxima and Minima of a function of one variables<\/strong><\/h2>\n\n\n\n<p>If&nbsp; f(x) is a single value function in a region R, then-<\/p>\n\n\n\n<p>Maxima is a maximum point&nbsp; if and only if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/AAmeRavyzph3nEFgOCL1_-HLwi25d-MrI-BS-QUbGM2O5cAqXY2wUIgq6I6qesvEFfXtW6d4JUr_XcSwkfILflSjWNL-HALeZlVTAqVfNzbkz4qKhweZku1VEapQA7TlD0E9zafLwYOIH6f3wg\" width=\"221\" height=\"33\"><\/p>\n\n\n\n<p>Minima is a minimum point&nbsp; if and only if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/7Lid2zhXrFXKmM860AaokPrRjnVeKDjXOg2YA1dMKIJyxt-hOcsbCw2Xe1ZAyE7rI-a5LLfs5QbKhmo85mQtLMBTPOY1vjFHicMQb-lVEioi_xVFWDVmbhUSXq8JE5IU_3f-O5HCMvjO8g4POQ\" width=\"221\" height=\"26\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction(Increasing and decreasing functions)- A function is said to be increasing function in an interval [a, b] if y increases as well&hellip;<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-7907","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What are the Increasing and decreasing functions? 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