{"id":3415,"date":"2024-06-24T16:33:37","date_gmt":"2024-06-24T16:33:37","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3415"},"modified":"2024-08-05T12:39:11","modified_gmt":"2024-08-05T12:39:11","slug":"the-derivative-as-a-function-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/the-derivative-as-a-function-apply-it\/","title":{"raw":"The Derivative as a Function: Apply It","rendered":"The Derivative as a Function: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Find the derivative of a function<\/li>\r\n\t<li>Draw the derivative's graph using the original function\u2019s graph<\/li>\r\n\t<li>Explain what it means for a function to be differentiable and how this is connected to being continuous<\/li>\r\n\t<li>Calculate derivatives beyond the first order<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h1 class=\"font-600 text-lg font-bold\">City Transportation Calculus: Analyzing Motion and Planning<\/h1>\r\n<p class=\"whitespace-pre-wrap break-words\">As a transportation engineer in a growing city, you're tasked with analyzing various aspects of movement and planning using calculus. Your insights will help improve traffic flow, design safer roads, and optimize public transportation. Let's explore how derivatives and their graphs can aid in understanding and solving real-world transportation challenges.<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288365[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288366[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288367[\/ohm_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Find the derivative of a function<\/li>\n<li>Draw the derivative&#8217;s graph using the original function\u2019s graph<\/li>\n<li>Explain what it means for a function to be differentiable and how this is connected to being continuous<\/li>\n<li>Calculate derivatives beyond the first order<\/li>\n<\/ul>\n<\/section>\n<h1 class=\"font-600 text-lg font-bold\">City Transportation Calculus: Analyzing Motion and Planning<\/h1>\n<p class=\"whitespace-pre-wrap break-words\">As a transportation engineer in a growing city, you&#8217;re tasked with analyzing various aspects of movement and planning using calculus. Your insights will help improve traffic flow, design safer roads, and optimize public transportation. Let&#8217;s explore how derivatives and their graphs can aid in understanding and solving real-world transportation challenges.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288365\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288365&theme=lumen&iframe_resize_id=ohm288365&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288366\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288366&theme=lumen&iframe_resize_id=ohm288366&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288367\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288367&theme=lumen&iframe_resize_id=ohm288367&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":503,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3415"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3415\/revisions"}],"predecessor-version":[{"id":4496,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3415\/revisions\/4496"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/503"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3415\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3415"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3415"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3415"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}