{"id":174418,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/how-do-you-determine-the-y-intercept-of-the-tangent-line-to-the-curve-ysqrtx24-at-x3"},"modified":"2018-10-24T09:34:54","modified_gmt":"2018-10-24T09:34:54","slug":"how-do-you-determine-the-y-intercept-of-the-tangent-line-to-the-curve-ysqrtx24-at-x3","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/how-do-you-determine-the-y-intercept-of-the-tangent-line-to-the-curve-ysqrtx24-at-x3\/","title":{"rendered":"How do you determine the y-intercept of the tangent line to the curve ##y=sqrt(x^2+4)## at ##x=3##?"},"content":{"rendered":"<p>to find the tangent line of the curve, take the derivative, to determine the slope of the tangent line.<\/p>\n<p>y=##sqrt(x^2+4)## y=##(x^2+4)^(1\/2)## y&#8217;=##1\/2####(x^2+4)^(-1\/2)##(2x) y&#8217;=##x\/sqrt(x^2+4)##<\/p>\n<p>because you want the tangent line at x=3, plug it in to y&#8217; to find the slop at that point, since we know that the derivative is the slope at a certain point.<\/p>\n<p>y'(3)=##3\/sqrt(3^2+4)##=##3\/sqrt(13)##<\/p>\n<p>at x=3, the point on the curve is (3,##sqrt13##) now, you can create the tangent line (y-##sqrt13##)= ##3\/sqrt13##(x-3) y-##sqrt13##=##3\/sqrt13##x-##9\/sqrt13## y=##3\/sqrt13##x-##9\/sqrt13##+##sqrt13##<\/p>\n<p>so your y-intercept for the tangent line at x=3 would be (##9\/sqrt13##+##sqrt13##) <\/p>\n","protected":false},"excerpt":{"rendered":"<p>to find the tangent line of the curve, take the derivative, to determine the slope of the tangent line. y=##sqrt(x^2+4)## y=##(x^2+4)^(1\/2)## y&#8217;=##1\/2####(x^2+4)^(-1\/2)##(2x) y&#8217;=##x\/sqrt(x^2+4)## because you want the tangent line at x=3, plug it in to y&#8217; to find the slop <a href=\"https:\/\/www.benedictsol.com\/blogs\/how-do-you-determine-the-y-intercept-of-the-tangent-line-to-the-curve-ysqrtx24-at-x3\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-174418","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/174418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=174418"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/174418\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=174418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=174418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=174418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}