{"id":33798,"date":"2020-04-03T11:38:18","date_gmt":"2020-04-03T15:38:18","guid":{"rendered":"https:\/\/www.myedme.com\/login\/?p=33798"},"modified":"2020-04-03T11:38:26","modified_gmt":"2020-04-03T15:38:26","slug":"slope-fields","status":"publish","type":"post","link":"https:\/\/myedme.com\/login\/slope-fields\/","title":{"rendered":"Slope Fields"},"content":{"rendered":"\n

Resources<\/strong> from OpenStax Calc II<\/a>
College Board YouTube
& Khan Academy Calc AB<\/p>\n\n\n\n

Slope Fields are a unit 7 topic that show the expected slope for any point in the x-y plane. You will not be asked to create these graphs but you may have to interpret them. <\/p>\n\n\n\n

\"\"<\/figure>
\n

A direction field (slope field)<\/strong> is a mathematical object used to graphically represent solutions to a first-order differential equation. At each point in a direction field, a line segment appears whose slope is equal to the slope of a solution to the differential equation passing through that point.<\/p>\n<\/div><\/div>\n\n\n\n

Example<\/h2>\n\n\n\n

An applied example of this type of differential equation appears in Newton\u2019s law of cooling, which we will solve explicitly later in this chapter. First, though, let us create a direction field for the differential equation.<\/p>\n\n\n\n

T\u2032(\ud835\udc61) = \u22120.4(\ud835\udc47\u221272)<\/p>\n\n\n\n

Here \ud835\udc47(\ud835\udc61)T(t) represents the temperature (in degrees Fahrenheit) of an object at time \ud835\udc61,t, and the ambient temperature is 72\u00b0F.72\u00b0F. Figure 4.6<\/a> shows the direction field for this equation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Resources from OpenStax Calc II College Board YouTube& Khan Academy Calc AB Slope Fields are a unit 7 topic that show the expected slope for any point in the x-y plane. You will not be asked to create these graphs but you may have to interpret them. A direction field (slope field) is a mathematical object used […]<\/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-33798","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\/33798","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=33798"}],"version-history":[{"count":2,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33798\/revisions"}],"predecessor-version":[{"id":33801,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33798\/revisions\/33801"}],"wp:attachment":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/media?parent=33798"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/categories?post=33798"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/tags?post=33798"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}