[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522868-105":59,"doc-detail-522868-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","normal-lines-calculus-practice-worksheet","Normal Lines - Calculus Practice Worksheet","","This calculus worksheet, developed by Kuta Software for their Infinite Calculus program, provides students with a series of practice problems focused on finding the equations of normal lines to various functions at specific coordinates. The document covers a diverse range of mathematical functions, including polynomial, rational, logarithmic, and trigonometric functions. Each problem requires students to calculate the slope of the normal line and provide the final answer in slope-intercept form, with specific instructions for identifying vertical normal lines when applicable. The worksheet is designed for educational assessment and skill reinforcement, offering clear examples for students to apply derivative rules to determine the normal line equation at a given point on a curve.",{"@graph":69,"@context":123},[70,84,106],{"@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/normal-lines-calculus-practice-worksheet/522868/",{"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/normal-lines-calculus-practice-worksheet/522868.png","ImageObject",300,407,{"name":92,"@type":93},"Angel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you define a normal line to a function at a point?","Question",{"text":113,"@type":114},"A normal line is a line perpendicular to the tangent line of a function at a specific point on the curve.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What format should the answers be in for this worksheet?",{"text":118,"@type":114},"Answers should be provided in slope-intercept form, unless the normal line is vertical, in which case it should be noted as a vertical line at a specific x-value.",{"name":120,"@type":111,"acceptedAnswer":121},"What types of functions are covered in these exercises?",{"text":122,"@type":114},"The exercises cover polynomial, rational, logarithmic, and trigonometric functions to help students practice applying derivative rules in various contexts.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522868,1791469675,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},687207412472,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Calculus Name   \nNormal Lines Date  Period   \nFor each problem, find the equation of the line normal to the function at the given point. If the normal line is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.  \n1) y = x 3 − x 2 − 2 at ( 1, −2)  \n3) y = − x 3 + 15x 2 − 72x + 110 at (4, −2) 2  \n4) y = x − 3 at (5, 1)  \n5) y = x~~ ~~~~ ~~2 at (4, ~~ ~~12) 6) y = (2x − 8)~~ ~~13 at (0, −2)  \n7) y = ln (x + 4) at (−3, 0) 8) y = −sin (2x) at (− ~~ ~~π2~~ ~~ , 0)  \nKuta Software-Infinite Calculus Name   \nNormal Lines Date  Period   \nFor each problem, find the equation of the line normal to the function at the given point. If the normal line is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.  \n1) y = x 3 − x 2 − 2 at ( 1, −2)  \ny = − x − 1  \n3) y = − x 3 + 15x 2 − 72x + 110 at (4, −2)  \nNormal line is vertical line at x = 4  \n5) y = x~~ ~~~~ ~~2 at (4, ~~ ~~12)  \ny = 12x − ~~ ~~952  \n7) y = ln (x + 4) at (−3, 0)  \ny = − x − 3  \n2) y = x~~ ~~~~ ~~4 at (5, 1)  \ny = x − 4  \n4) y = x~~ ~~~~ ~~3 at (5, 1)  \ny = 2x − 9  \n 1   \n6) y = (2x − 8) 3 at (0, −2)  \ny = −6x − 2  \n8) y = −sin (2x) at (− ~~ ~~π2~~ ~~ , 0)  \ny = − ~~ ~~12x − π4  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaipHmjoYVicNq","https://ap.wps.com/l/cbCaipHmjoYVicNq","pdf",31355,"English","# Normal Line Practice Problems\n## Problem Descriptions\n## Answer Key","[{\"question\":\"How do you define a normal line to a function at a point?\",\"answer\":\"A normal line is a line perpendicular to the tangent line of a function at a specific point on the curve.\"},{\"question\":\"What format should the answers be in for this worksheet?\",\"answer\":\"Answers should be provided in slope-intercept form, unless the normal line is vertical, in which case it should be noted as a vertical line at a specific x-value.\"},{\"question\":\"What types of functions are covered in these exercises?\",\"answer\":\"The exercises cover polynomial, rational, logarithmic, and trigonometric functions to help students practice applying derivative rules in various contexts.\"}]","Normal Lines - Calculus Practice Worksheet | PDF",1791426253]