{"id":65067,"date":"2023-03-20T10:45:17","date_gmt":"2023-03-20T13:45:17","guid":{"rendered":"https:\/\/militares.estrategia.com\/portal\/?p=65067"},"modified":"2023-03-20T10:45:22","modified_gmt":"2023-03-20T13:45:22","slug":"como-classificar-a-monotonicidade-de-uma-funcao","status":"publish","type":"post","link":"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/","title":{"rendered":"Fun\u00e7\u00f5es: como classificar a monotonicidade?"},"content":{"rendered":"\n<p>Se voc\u00ea est\u00e1 estudando para os seletivos militares, sabe a dificuldade das avalia\u00e7\u00f5es! Ent\u00e3o, confira mais <strong>este resumo de Matem\u00e1tica sobre Fun\u00e7\u00f5es e os tipos de monotonicidade.<\/strong> O conte\u00fado \u00e9 baseado nas aulas do professor Victor So.&nbsp;<\/p>\n\n\n\n<p><a href=\"https:\/\/militares.estrategia.com\/portal\/materias-e-dicas\/matematica\/o-que-e-funcao\/\" target=\"_blank\" >Fun\u00e7\u00f5es<\/a> s\u00e3o tipos de rela\u00e7\u00f5es bin\u00e1rias, que sempre seguem as duas regras a seguir:\u00a0<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/jecWFFRE_2uHjTNBLDMXQdoANghDKp4BF6BbYMIULj5FsFxNWXfJQhV1JH64t7gNVaF4x0kA8s9R3NBMLnZ4xpSHBcmab-zZ3rIjgv3YOWYXkt3qLPBF3icrQsReAHxwrCjTwCyjKz7aklPczIeSVZw\" alt=\"\" width=\"527\" height=\"427\"\/><\/figure><\/div>\n\n\n<p>Quando falamos de<strong> monotonicidade, trata-se de como classificar as fun\u00e7\u00f5es de acordo com seu comportamento em determinado intervalo.<\/strong> Vamos ver as possibilidades abaixo!&nbsp;<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_2 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Navegue pelo conte\u00fado\t<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Crescente\" >Crescente<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Decrescente\" >Decrescente<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Constante\" >Constante<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Estritamente-Crescente\" >Estritamente Crescente<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Estritamente-Decrescente\" >Estritamente Decrescente<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Monotonicidade-da-Funcao-Afim\" >Monotonicidade da Fun\u00e7\u00e3o Afim<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Com-%F0%9D%91%93-crescente\" >Com \ud835\udc53 crescente<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/militares.estrategia.com\/portal\/noticias\/como-classificar-a-monotonicidade-de-uma-funcao\/#Com-%F0%9D%91%93-decrescente\" >Com \ud835\udc53 decrescente<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-crescente\"><span class=\"ez-toc-section\" id=\"Crescente\"><\/span>Crescente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Acontece quando<strong> o ponto final da fun\u00e7\u00e3o \u00e9 maior do que o inicial e a fun\u00e7\u00e3o n\u00e3o decresce dentro desse intervalo<\/strong>. A regra da fun\u00e7\u00e3o crescente \u00e9 a seguinte:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/c3Yxm1tVTgJzTNPR6b9IlcDjn7eDrGGH_kW8iByIp-adkkxQox-RAL1g7MlnRhKUNTIDzFNmMqrLj4OZK0HCkO4CijCox7J9yA7o_agcLHzRcUyQb5rSwaOJV54lNSDvyNQjHSc6NAMloQSceGeEphE\" alt=\"\" width=\"-35\" height=\"-2\"\/><\/figure><\/div>\n\n\n<p>Para melhor visualiza\u00e7\u00e3o, confira o gr\u00e1fico a seguir:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/1aQjAgZmf_3u75jsfcxEJXmBKDHvh-TW5VEG1c3x-80XJf6vNvrn89qKTEPHrfkl9pWrp_DazA9Lpm0CJceZhDMizWlf9mqJ6BveKDkK1b1su2jPO6eyUZpBAJtxokFVgPK9-QZkPcNQQ88vFbxCtb0\" alt=\"\" width=\"-154\" height=\"-137\"\/><\/figure><\/div>\n\n\n<p>Assim, \ud835\udc53 \u00e9 crescente em \ud835\udc3c = [1,3]. Do gr\u00e1fico, temos: \ud835\udc65<sub>1<\/sub> &lt; \ud835\udc65<sub>2<\/sub> &lt; \ud835\udc65<sub>3<\/sub> \u21d2 \ud835\udc53(\ud835\udc65<sub>1<\/sub>) = \ud835\udc53(\ud835\udc65<sub>2<\/sub>) &lt; \ud835\udc53(\ud835\udc65<sub>3<\/sub>). Perceba que<strong> entre 1 e x<\/strong><strong><sub>1<\/sub><\/strong><strong>, a fun\u00e7\u00e3o \u00e9 constante e entre x<\/strong><strong><sub>2<\/sub><\/strong><strong> e 3, a fun\u00e7\u00e3o \u00e9 estritamente crescente.&nbsp;<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-decrescente\"><span class=\"ez-toc-section\" id=\"Decrescente\"><\/span>Decrescente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Da mesma forma, <strong>a fun\u00e7\u00e3o n\u00e3o cresce ao longo do intervalo e o ponto inicial \u00e9 maior que o ponto final.<\/strong> A regra da fun\u00e7\u00e3o decrescente \u00e9:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/cxbSCDtjs2bfaMFaq7UJTJxNCe1vjy1pvnOxiujVHTtKbQSi6M-KAbo8nYqj3DyxPNuOldqDl4qX5HGiB8UQ8CkkQSIZ1a1r5IqYV6AFIjnOEG19SucEUNZKB-ZIl5N3amlYbL3c50LGPis4xTuhsus\" alt=\"\" width=\"598\" height=\"65\"\/><\/figure><\/div>\n\n\n<p>Veja o exemplo gr\u00e1fico:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/nni4SxWOMzMgXlmi0f1pneseFu1WNaQsGwPuVNu1uLaxvBV-zcgzW1gs4PFGsQjBZaymrfotMG7_rkiCz92lAnTvZtc0PBMqbGA-f8VLPp-Rgmf7_Q_n63UoJWcNGqV99lwS07oxBjaxUiuv6M7cd0E\" alt=\"\" width=\"-112\" height=\"-100\"\/><\/figure><\/div>\n\n\n<p>Assim, \ud835\udc53 \u00e9 decrescente em \ud835\udc3c = [1,3]. Do gr\u00e1fico, temos que: \ud835\udc65<sub>1<\/sub> &lt; \ud835\udc65<sub>2<\/sub> &lt; \ud835\udc65<sub>3<\/sub> \u21d2 \ud835\udc53(\ud835\udc65<sub>1<\/sub>) = \ud835\udc53(\ud835\udc65<sub>2<\/sub>) &gt; \ud835\udc53(\ud835\udc65<sub>3<\/sub>). A fun\u00e7\u00e3o n\u00e3o cresce em nenhum momento ao longo do intervalo <em>I<\/em>. <strong>Perceba que entre 1 e \ud835\udc65<\/strong><strong><sub>1<\/sub><\/strong><strong>, a fun\u00e7\u00e3o \u00e9 constante e entre \ud835\udc65<\/strong><strong><sub>2<\/sub><\/strong><strong> e 3, a fun\u00e7\u00e3o \u00e9 estritamente decrescente.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-constante\"><span class=\"ez-toc-section\" id=\"Constante\"><\/span>Constante<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Neste caso, a regra \u00e9:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/AyH7EWiiWi81ZIlKRrXohEqd46OPCmVcwJf526qkgeHYkO8lhugH8oJib5pXKZZb3sNvQXTueL3cacdrb0JBm_PPQYahgtSB4jcKmC8P_d3OZSJ-veS2qn317vMC6k1C4JLvaKQuJWD5nrMXdSEyXU0\" alt=\"\"\/><\/figure>\n\n\n\n<p>Assim, o exemplo gr\u00e1fico \u00e9:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/ZfftCkXsZ5O55CDIcCOW8XABOhsFm_cizoX6i5mch2GedBtfG-EvAxlJsuoQHKWaO844f31LrDR_bolWLY1BaD1YDIYG4JyDvD6oPxk6AHMAirju8Q4LRFKCsQ1OnYtahqxsMtEga7sgC3s9U6pTKNY\" alt=\"\"\/><\/figure>\n\n\n\n<p>Como vimos, a fun\u00e7\u00e3o \ud835\udc53 \u00e9 constante no intervalo \ud835\udc3c. Em que:&nbsp;<\/p>\n\n\n\n<p>\u2200\ud835\udc65<sub>1<\/sub>, \ud835\udc65<sub>2<\/sub> \u2208 \ud835\udc3c, \ud835\udc53(\ud835\udc65<sub>1<\/sub>) = \ud835\udc53(\ud835\udc65<sub>2<\/sub>) = \ud835\udc50<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-estritamente-crescente\"><span class=\"ez-toc-section\" id=\"Estritamente-Crescente\"><\/span>Estritamente Crescente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>No caso da fun\u00e7\u00e3o estritamente crescente,<strong> n\u00e3o h\u00e1 trechos constantes ou decrescentes. <\/strong>Assim, a regra \u00e9:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Eq_ck10JMUjfhLsxBlydDs4giUeVB2BrVBYDa1SlqhS8lMAQC6Vt8juKcOH0ioGV0MOLSlvpdUwyYI-7GZ8MEtM4z46h6gvN8t1tzoOxQ2cZMZUQEoo6yS1I9Y8JSK56o1aN0bzJLxdeMrNJ7E4ig00\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>O exemplo gr\u00e1fico \u00e9:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/0JkafeHEcdmoMBq7u09r-YPOnzutfSHsG0HpfZAQ6JPe9KjrBL9V7nClUqePm3MVCtG2azEAgkcC214HJ3SNboFKjuCwrfZAuhGI8nRrKSPoPkT07_LT6UCbB4y716V_LhTbYaVI7d_0jbjifrbuAC4\" alt=\"\" width=\"-24\" height=\"-26\"\/><\/figure><\/div>\n\n\n<p>Logo<strong>, \ud835\udc53 \u00e9 estritamente crescente em \ud835\udc3c. <\/strong>Para qualquer \ud835\udc65<sub>1<\/sub> &lt; \ud835\udc65<sub>2<\/sub> \u2208 \ud835\udc3c, temos \ud835\udc53(\ud835\udc65<sub>1<\/sub>) &lt; \ud835\udc53(\ud835\udc65<sub>2<\/sub>).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-estritamente-decrescente\"><span class=\"ez-toc-section\" id=\"Estritamente-Decrescente\"><\/span>Estritamente Decrescente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A fun\u00e7\u00e3o estritamente decrescente pode ser descrita assim:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/HCkcfZw_E21wCvWpYWSFJyiUylDQ9LGJMOnkfpqCqUrUwSYHNAHWigM53O58-wbdy4pLs5oM_8Hg8eubCo_i63ywlU-msXxci355DLLD5eanVYmuBdxdnexGBqdgtiFxy-FvXqOkhZ0NWbpOUfijsEQ\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>O exemplo gr\u00e1fico seria o seguinte:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/pbuUPT-Y9_6jJRyfSJKxCJhZUXpy298KZPWm844TO1KyxZMGR0Ygcqn2ItGSvgoCeFOZ4k2V5P6UFoJd8bCN6-G5CpMpX9MDzqCP2ViByNLOENOaTfbJ8xPRs5gJkAQ3n6EwXSzSI3lJIXCsGAyCWzM\" alt=\"\" width=\"-40\" height=\"-43\"\/><\/figure><\/div>\n\n\n<p>Assim, <strong>\ud835\udc53 \u00e9 estritamente decrescente em \ud835\udc3c.<\/strong> Para qualquer \ud835\udc65<sub>1<\/sub> &lt; \ud835\udc65<sub>2<\/sub> \u2208 \ud835\udc3c, temos \ud835\udc53(\ud835\udc65<sub>2<\/sub>) &lt; \ud835\udc53(\ud835\udc65<sub>1<\/sub>).&nbsp;<\/p>\n\n\n\n<p>Depois de ver as classifica\u00e7\u00f5es acima, \u00e9 importante guardar a seguinte informa\u00e7\u00e3o: <strong>uma fun\u00e7\u00e3o \ud835\udc53 \u00e9 dita mon\u00f3tona se for crescente ou decrescente<\/strong>; por\u00e9m, <strong>se \ud835\udc53 for estritamente crescente ou estritamente decrescente, ela \u00e9 dita estritamente mon\u00f3tona.&nbsp;<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-monotonicidade-da-funcao-afim\"><span class=\"ez-toc-section\" id=\"Monotonicidade-da-Funcao-Afim\"><\/span>Monotonicidade da Fun\u00e7\u00e3o Afim<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Agora, como \u00e9 poss\u00edvel identificar a monotonicidade da <a href=\"https:\/\/militares.estrategia.com\/portal\/materias-e-dicas\/matematica\/o-que-e-funcao-afim\/\" target=\"_blank\" >fun\u00e7\u00e3o afim<\/a>? Considere \ud835\udc53: \u211d \u2192 \u211d, \ud835\udc53(\ud835\udc65) = \ud835\udc4e\ud835\udc65 + \ud835\udc4f, \ud835\udc4e \u2260 0. Vamos<strong> analisar a monotonicidade da fun\u00e7\u00e3o afim n\u00e3o constante.<\/strong> Tomando \ud835\udc65<sub>1<\/sub>, \ud835\udc65<sub>2<\/sub> \u2208 \u211d, temos:\u00a0<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc53(\ud835\udc65<sub>1<\/sub>) = \ud835\udc4e\ud835\udc65<sub>1<\/sub> + \ud835\udc4f<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc53(\ud835\udc65<sub>2<\/sub>) = \ud835\udc4e\ud835\udc65<sub>2<\/sub> + \ud835\udc4f<\/p>\n\n\n\n<p>Ao subtrair as duas equa\u00e7\u00f5es temos:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/1cgcJ1so8Wqcq_HyGk8vjQLMzG93PRbzOS_wJhEQU05eAJu6QlQhflnC00S89svlp7G-G-fO7A1nSEu-cD4Pjgtrl-CL_TWprCTCdjpCCSNXRfv4p1fKxq3QYk_EbUczi7grlbV-kK7IGKUOPLIOU7E\" alt=\"\" width=\"222\" height=\"96\"\/><\/figure><\/div>\n\n\n<p>A partir daqui, vamos analisar o sinal do coeficiente angular \ud835\udc4e para \ud835\udc53 crescente e decrescente:&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-com-\ud835\udc53-crescente\"><span class=\"ez-toc-section\" id=\"Com-%F0%9D%91%93-crescente\"><\/span>Com \ud835\udc53 crescente<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Sendo \ud835\udc53(\ud835\udc65) = \ud835\udc4e\ud835\udc65 + \ud835\udc4f, uma fun\u00e7\u00e3o crescente, podemos escrever:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc65<sub>2<\/sub> &gt; \ud835\udc65<sub>1<\/sub> \u21d2 \ud835\udc53(\ud835\udc65<sub>2<\/sub>) &gt; \ud835\udc53(\ud835\udc65<sub>1<\/sub>)<\/p>\n\n\n\n<p>Das desigualdades acima:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc65<sub>2<\/sub> &gt; \ud835\udc65<sub>1<\/sub> \u21d2 \ud835\udc65<sub>2<\/sub> \u2212 \ud835\udc65<sub>1<\/sub> &gt; 0<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc53(\ud835\udc65<sub>2<\/sub>) &gt; \ud835\udc53(\ud835\udc65<sub>1<\/sub>) \u21d2 \ud835\udc53(\ud835\udc65<sub>2<\/sub>) \u2212 \ud835\udc53(\ud835\udc65<sub>1<\/sub>) &gt; 0<\/p>\n\n\n\n<p>Isso implica em:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/dXjhLc0xtxosmX_xuVWUKckp9sknUm2pZzZqqapUujB0h_7lqlkLKuKFBhbrWEOQ7n1zOmRdj-I2OCoYV9CZichJZ7D4gbpXDtDeaKjG4SWVbEv0HwXO8yaTXSYEwwguyFhv7vSZc85u1RjJgal-v2E\" alt=\"\" width=\"154\" height=\"60\"\/><\/figure><\/div>\n\n\n<p>Se o coeficiente angular \u00e9 dado por:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Pwr2EffqRrOihpi8hHZ-QI_uL9T1c2FB3FrPvb8Z-F0LbY2Zj3nXMvcy7AvHZqopnqyOUmO5-sQj4TdPM2hA5l8AZ3u7jkKs3XLpbVegow1EDHT0j0EqxGZYRGRr_wB_vPf3snMymKxl5l4OH0ws350\" alt=\"\" width=\"189\" height=\"61\"\/><\/figure><\/div>\n\n\n<p>Assim, conclu\u00edmos que:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/mwbuD8g_SaVyw0tdA1DXnx4sld49yqTBGwpqcJQLMP9lPN1aCvCxDSQrh-BnUtDdTpV8vPU4y4yz2hvhP9Vo1XcnntN7dizQeRBv7l7N7Al6TtYcx0YTWScJ8jf-sLVWTLSc4NARshTTR3DP2p7Va7A\" alt=\"\" width=\"209\" height=\"26\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-com-\ud835\udc53-decrescente\"><span class=\"ez-toc-section\" id=\"Com-%F0%9D%91%93-decrescente\"><\/span>Com \ud835\udc53 decrescente<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Sendo \ud835\udc53(\ud835\udc65) = \ud835\udc4e\ud835\udc65 + \ud835\udc4f, uma fun\u00e7\u00e3o decrescente, podemos escrever:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc65<sub>2<\/sub> &gt; \ud835\udc65<sub>1<\/sub> \u21d2 \ud835\udc53(\ud835\udc65<sub>2<\/sub>) &lt; \ud835\udc53(\ud835\udc65<sub>1<\/sub>)<\/p>\n\n\n\n<p>Das desigualdades acima:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc65<sub>2<\/sub> &gt; \ud835\udc65<sub>1<\/sub> \u21d2 \ud835\udc65<sub>2<\/sub> \u2212 \ud835\udc65<sub>1<\/sub> &gt; 0<\/p>\n\n\n\n<p class=\"has-text-align-center\">\ud835\udc53(\ud835\udc65<sub>2<\/sub>) &lt; \ud835\udc53(\ud835\udc65<sub>1<\/sub>) \u21d2 \ud835\udc53(\ud835\udc65<sub>2<\/sub>) \u2212 \ud835\udc53(\ud835\udc65<sub>1<\/sub>) &lt; 0<\/p>\n\n\n\n<p>Isso implica em:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/IaDfDYK99B4wRPy8qDNg9TQCAHw3zKFo9Qy-Zd2GANERzQAlvEHSTwn7pObfGNh0-WbcNZm0m-YfS-H9ONztZyAfePOuSX5BJLKu6xoz_VhC2-ew8IHT-kQH4208PtqkJUCAaEHmqqIOvqEhh0FU2dk\" alt=\"\" width=\"164\" height=\"62\"\/><\/figure><\/div>\n\n\n<p>Se o coeficiente angular \u00e9 dado por:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/zhGd_yGv4uWoI2FTYhBh5e0ty6ibrWlCo50IMQUUzpNKZbMUepwFzqKknjvnQJSC3CL6XTdnG8O3NX7240WOGIc45viCdnNPlwIpeZzUIABLV4A4dnnC7cA3qPigO-pwwhi3ddq8D48lIe6EkRgRE1k\" alt=\"\" width=\"-104\" height=\"-34\"\/><\/figure><\/div>\n\n\n<p>Logo, podemos dizer que:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/JgMyxs3smkoNRjYCu5QZw14tLbeKFjIlOsaKJGc_TGUG9UQGUjxcC6l-tRChEzgneuaEXDdvRa_oWdWmWltLldLJqBvAyKHfp1Ci5Yia74bsX-SSQGj9OFpWGWPR1yGZGjOekFc-lZXHc4EOjgwW0aQ\" alt=\"\" width=\"-2\" height=\"0\"\/><\/figure><\/div>\n\n\n<p>Para resumir, ent\u00e3o, podemos esquematizar a monotonicidade da Fun\u00e7\u00e3o Afim da seguinte forma:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/v7Y3lJJHYYKU5KxA-Vhqzf70wY8abebE6zfdIWNvCTOxJ5FxBRMkZYKQnboRWDbbKHpS4-zHJ9Wd6dzw6w00XBaHPGzQmadt3PeS84iXceKXxcLzKYEZrPmYtr0ONvGslmOnnaq3lSJlE1kcaSOMPMM\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Se voc\u00ea quiser praticar seus conhecimentos, conhe\u00e7a o Banco de Quest\u00f5es do Estrat\u00e9gia Militares e tenha acesso a milhares de simulados e provas militares! Clique no banner e saiba mais!<\/p>\n","protected":false},"excerpt":{"rendered":"Se voc\u00ea est\u00e1 estudando para os seletivos militares, sabe a dificuldade das avalia\u00e7\u00f5es! Ent\u00e3o, confira mais este resumo&hellip;\n","protected":false},"author":9,"featured_media":65068,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"wl_entities_gutenberg":"","footnotes":""},"categories":[36],"tags":[],"wl_entity_type":[187],"class_list":{"0":"post-65067","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-noticias","8":"wl_entity_type-article"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.6 (Yoast SEO v26.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fun\u00e7\u00f5es: como classificar a monotonicidade?<\/title>\n<meta name=\"description\" content=\"Entenda o conte\u00fado de fun\u00e7\u00f5es e como classificar a sua monotonicidade com este resumo que o Estrat\u00e9gia Militares separou para voc\u00ea!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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