[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522857-105":59,"doc-detail-522857-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","horizontal-tangents-calculus-practice-worksheet","Horizontal Tangents - Calculus Practice Worksheet","","This document provides a set of calculus practice problems focused on identifying points where the tangent line to a given function is horizontal. The content includes a series of polynomial and trigonometric function expressions, requiring students to apply derivative analysis to locate stationary points or determine if such points exist within specific intervals. It serves as an educational worksheet for students studying differential calculus, offering both problem statements and corresponding coordinate solutions for review and mastery of horizontal tangent concepts.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/horizontal-tangents-calculus-practice-worksheet/522857/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/horizontal-tangents-calculus-practice-worksheet/522857.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn Holloway","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-14","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find points where the tangent line to a function is horizontal?","Question",{"text":112,"@type":113},"To find horizontal tangents, you must calculate the derivative of the function, set it equal to zero, and solve for x. The resulting x-values are then substituted back into the original function to find the corresponding y-coordinates.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What should be indicated if no horizontal tangent line exists for a function?",{"text":117,"@type":113},"If the derivative of a function has no real roots, then the function has no points where the slope is zero. In such cases, it should be clearly noted that no horizontal tangent line exists.",{"name":119,"@type":110,"acceptedAnswer":120},"Are there specific constraints for finding horizontal tangents in trigonometric functions?",{"text":121,"@type":113},"Yes, for trigonometric functions like cosecant, the problem may specify an interval, such as [−π, π], within which you must evaluate the derivative to identify valid points where the tangent line is horizontal.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522857,1791490302,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},2336474466712,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Calculus Name   \nHorizontal Tangents Date  Period   \nFor each problem, find the points where the tangent line to the function is horizontal.  \n1) y = − x 2 − 4x − 6  \n2) y = − x 3 + 3x 2 − 1  \n3) y = − x 3 + x 2 − 2  1   \n4) y = 2  \nx − 1  \nFor each problem, find the points where the tangent line to the function is horizontal. Indicate if no horizontal tangent line exists.  \n5) y = x 3 − 2x 2 + 2 3 9x2  \n6) y = − x +  2  − 12x − 3  \n7) y = −  2  8) y = −  1  x − 3 x 2 + 1  \n1  10) y = −csc (x) ; [−π , π]  \n9) y = (−2x + 4) 2  \nKuta Software-Infinite Calculus Name   \nHorizontal Tangents Date  Period   \nFor each problem, find the points where the tangent line to the function is horizontal.  \n1) y = − x 2 − 4x − 6  \n(−2, −2)  \n2) y = − x 3 + 3x 2 − 1  \n(0, −1), (2, 3)  \n3) y = − x 3 + x 2 − 2  1   \n4) y = 2  \n(0, −2),(~~ ~~23~~ ~~ , − ~~ ~~5027) (0,x− ) 1  \nFor each problem, find the points where the tangent line to the function is horizontal. Indicate if no horizontal tangent line exists.  \n5) y = x 3 − 2x 2 + 2 9x2  \n6) y = − x 3 + ~~ ~~ − 12x − 3  \n(0, 2),(~~ ~~43~~ ~~ , ~~ ~~2227) No horizo2ntal tangent line exists.  \n7) y = − ~~ ~~x~~ ~~~~ ~~3~~ ~~ 8) y = − ~~ ~~x~~ ~~2~~ ~~~~ ~~1  \nNo horizontal tangent line exists. (0, −1)  \n1  10) y = −csc (x) ; [−π , π]  \n9) y = (−2x + 4) 2  \nNo horizontal tangent line exists. (− ~~ ~~π2~~ ~~ , 1),(~~ ~~π2~~ ~~ , −1)  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCailGUhGLUdaYd","https://ap.wps.com/l/cbCailGUhGLUdaYd","pdf",73696,"English","# Practice Problems\n## Solutions and Answers","[{\"question\":\"How do you find points where the tangent line to a function is horizontal?\",\"answer\":\"To find horizontal tangents, you must calculate the derivative of the function, set it equal to zero, and solve for x. The resulting x-values are then substituted back into the original function to find the corresponding y-coordinates.\"},{\"question\":\"What should be indicated if no horizontal tangent line exists for a function?\",\"answer\":\"If the derivative of a function has no real roots, then the function has no points where the slope is zero. In such cases, it should be clearly noted that no horizontal tangent line exists.\"},{\"question\":\"Are there specific constraints for finding horizontal tangents in trigonometric functions?\",\"answer\":\"Yes, for trigonometric functions like cosecant, the problem may specify an interval, such as [−π, π], within which you must evaluate the derivative to identify valid points where the tangent line is horizontal.\"}]","Horizontal Tangents - Calculus Practice Worksheet | PDF",1791426241]