{"id":33952,"date":"2020-04-20T12:14:16","date_gmt":"2020-04-20T16:14:16","guid":{"rendered":"https:\/\/www.myedme.com\/login\/?p=33952"},"modified":"2020-04-20T12:14:24","modified_gmt":"2020-04-20T16:14:24","slug":"derivatives-of-absolute-values","status":"publish","type":"post","link":"https:\/\/myedme.com\/login\/derivatives-of-absolute-values\/","title":{"rendered":"Derivatives of Absolute Values"},"content":{"rendered":"\n<p>Remember absolute values are really two functions. For example, if |x + 2| = 3, then we find both solutions by solving x + 2 = 3 and x + 2 = -3 (put x = 1 and x = -5 to the original equation to check yourself). <\/p>\n\n\n\n<p>This is complicated, so it&#8217;s worthwhile to specifically consider linear functions. The derivative is the rate of change. For linear equation, the rate of change <strong>is<\/strong> the slope. So, if we need to take the derivative of y =|x + 2|, then we can see the slope is 1 when x greater than -2. The slope is -1 when x is less than -2.    <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1199\" height=\"515\" src=\"https:\/\/i2.wp.com\/www.myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?fit=980%2C421&amp;ssl=1\" alt=\"\" class=\"wp-image-33953\" srcset=\"https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?w=1199&amp;ssl=1 1199w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=300%2C129&amp;ssl=1 300w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=1024%2C440&amp;ssl=1 1024w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=768%2C330&amp;ssl=1 768w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=50%2C21&amp;ssl=1 50w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=100%2C43&amp;ssl=1 100w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/image-5.png?resize=416%2C179&amp;ssl=1 416w\" sizes=\"auto, (max-width: 980px) 100vw, 980px\" \/><figcaption>The graph of y = |x+2| has two slopes. The blue line shows the graph of the derivative for each x-value (note that the function is not differentiable at x=-2).<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Video Overview<\/h2>\n\n\n\n<p>This video shows how to find derivatives of linear and quadratic absolute functions. <\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><div  id=\"_ytid_27604\"  width=\"980\" height=\"551\"  data-origwidth=\"980\" data-origheight=\"551\" data-facadesrc=\"https:\/\/www.youtube.com\/embed\/eIHtq67nh7w?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__ epyt-facade epyt-is-override  no-lazyload\" data-epautoplay=\"1\" ><img data-recalc-dims=\"1\" decoding=\"async\" data-spai-excluded=\"true\" class=\"epyt-facade-poster skip-lazy\" loading=\"lazy\"  alt=\"YouTube player\"  src=\"https:\/\/i0.wp.com\/i.ytimg.com\/vi\/eIHtq67nh7w\/maxresdefault.jpg?w=980&#038;ssl=1\"  \/><button class=\"epyt-facade-play\" aria-label=\"Play\"><svg data-no-lazy=\"1\" height=\"100%\" version=\"1.1\" viewBox=\"0 0 68 48\" width=\"100%\"><path class=\"ytp-large-play-button-bg\" d=\"M66.52,7.74c-0.78-2.93-2.49-5.41-5.42-6.19C55.79,.13,34,0,34,0S12.21,.13,6.9,1.55 C3.97,2.33,2.27,4.81,1.48,7.74C0.06,13.05,0,24,0,24s0.06,10.95,1.48,16.26c0.78,2.93,2.49,5.41,5.42,6.19 C12.21,47.87,34,48,34,48s21.79-0.13,27.1-1.55c2.93-0.78,4.64-3.26,5.42-6.19C67.94,34.95,68,24,68,24S67.94,13.05,66.52,7.74z\" fill=\"#f00\"><\/path><path d=\"M 45,24 27,14 27,34\" fill=\"#fff\"><\/path><\/svg><\/button><\/div><\/div>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Remember absolute values are really two functions. For example, if |x + 2| = 3, then we find both solutions by solving x + 2 = 3 and x + 2 = -3 (put x = 1 and x = -5 to the original equation to check yourself). This is complicated, so it&#8217;s worthwhile to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33952","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33952","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/comments?post=33952"}],"version-history":[{"count":1,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33952\/revisions"}],"predecessor-version":[{"id":33954,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33952\/revisions\/33954"}],"wp:attachment":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/media?parent=33952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/categories?post=33952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/tags?post=33952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}