{"id":27101,"date":"2025-06-19T20:55:52","date_gmt":"2025-06-19T20:55:52","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27101"},"modified":"2025-06-19T20:55:57","modified_gmt":"2025-06-19T20:55:57","slug":"you-are-given-the-graph-of-function-f","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/you-are-given-the-graph-of-function-f\/","title":{"rendered":"You are given the graph of function f."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">You are given the graph of function f. Determine the relative maxima and relative minima, if any: (If an answer does not exist, enter DNE:) relative minimum smaller x-value (x, Y) relative minimum larger x-value (x, Y) relative maximum (x,Y) =<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Correct Answers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Relative minimum smaller x-value (x,y)=(\u22124,0)(x, y) = (-4, 0)(x,y)=(\u22124,0)<\/li>\n\n\n\n<li>Relative minimum larger x-value (x,y)=(4,0)(x, y) = (4, 0)(x,y)=(4,0)<\/li>\n\n\n\n<li>Relative maximum (x,y)=(0,3)(x, y) = (0, 3)(x,y)=(0,3)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Explanation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To identify relative extrema (minimums and maximums) from the graph of a function, we need to observe the peaks and valleys of the graph within the given interval. A <strong>relative maximum<\/strong> is a point where the function value is higher than the values immediately around it. A <strong>relative minimum<\/strong> is a point where the function value is lower than the values around it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Looking at the graph provided:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>At x=\u22124x = -4x=\u22124<\/strong>:<br>The function reaches a low point at (x,y)=(\u22124,0)(x, y) = (-4, 0)(x,y)=(\u22124,0). As we move away from x=\u22124x = -4x=\u22124 toward x=0x = 0x=0, the y-values increase. This indicates that (\u22124,0)(-4, 0)(\u22124,0) is a <strong>relative minimum<\/strong> because it is lower than its surrounding values.<\/li>\n\n\n\n<li><strong>At x=0x = 0x=0<\/strong>:<br>The function peaks at (0,3)(0, 3)(0,3). As you move both to the left and to the right from this point, the function values decrease, forming a &#8220;peak&#8221; at x=0x = 0x=0. Therefore, (0,3)(0, 3)(0,3) is a <strong>relative maximum<\/strong>.<\/li>\n\n\n\n<li><strong>At x=4x = 4x=4<\/strong>:<br>Just like at x=\u22124x = -4x=\u22124, the point (4,0)(4, 0)(4,0) is a valley. The function decreases toward this point and then increases afterward. Hence, (4,0)(4, 0)(4,0) is another <strong>relative minimum<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">In conclusion, the function has <strong>two relative minima<\/strong> at (\u22124,0)(-4, 0)(\u22124,0) and (4,0)(4, 0)(4,0), and <strong>one relative maximum<\/strong> at (0,3)(0, 3)(0,3). These points represent local valleys and a peak within the domain of the function shown.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-143.jpeg\" alt=\"\" class=\"wp-image-27106\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-143.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-143-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-143-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>You are given the graph of function f. Determine the relative maxima and relative minima, if any: (If an answer does not exist, enter DNE:) relative minimum smaller x-value (x, Y) relative minimum larger x-value (x, Y) relative maximum (x,Y) = The Correct Answer and Explanation is: Correct Answers: Explanation To identify relative extrema (minimums [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27101","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27101"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27101\/revisions"}],"predecessor-version":[{"id":27107,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27101\/revisions\/27107"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}