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Each is stated with the conditions needed on continuity and derivatives.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which differentiation rules and derivative facts are summarized?",{"text":118,"@type":114},"It lists the chain rule, product rule, and quotient rule, along with an alternate definition of the derivative and a set of basic derivative formulas for standard functions.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the document guide curve sketching and finding maxima/minima?",{"text":122,"@type":114},"It instructs how to use critical points and endpoints, the sign changes of the first derivative for relative extrema, and the second derivative for concavity and inflection points. It also includes horizontal asymptote rules and tangent line setup.","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},311442,1789894292,{"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":44,"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":130,"read_time":105,"preview_page_count":4},2336475104362,"https://ap-avatar.wpscdn.com/avatar/22000c4c46a41b752dd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786595829695023868","AP CALCULUS AB STUFF YOU  \nMUST KNOW COLD  \nThanks for downloading my products!  \nAs you prepare your students for the AP Calculus AB Exam, here’s an adaptation to Sean Bird’s“Stuff You Must Know Cold” handout. ( [http://covenantchristian.org/bird/Calculus.htm](http://covenantchristian.org/bird/Calculus.htm) ) Formulas, Theorems, and Other concepts necessary for success for the Calculus AB student. You will find additional resources, including a PowerPoint version, a Word document in color, as well as AP Calculus BC topics on his website.  \nIf you like this product, you might enjoy my Calculus Target Practice. Follow this link to preview the packet  \n[http://www.teacherspayteachers.com/Product/AP-Calculus-AB-Target-Practice-1210286](http://www.teacherspayteachers.com/Product/AP-Calculus-AB-Target-Practice-1210286)  \n[You might want to visit my store for more engaging lessons and review materials.](You might want to visit my store for more engaging lessons and review materials.)  \n[http://www.teacherspayteachers.com/Store/Jean-Adams](http://www.teacherspayteachers.com/Store/Jean-Adams)  \nCredits:  \nPolka Dot Background  \nSTUFF YOU MUST KNOW COLD . . .  \nAlternate Definition of the Derivative:  \n′ 􀝂 (􀝔) − 􀝂 (􀜿)  \n􀝂 (􀜿) = lim ~~ ~~  \n􀯫 →􀯖 􀝔 − 􀜿  \n\n| Basic Derivatives\u003Cbr>􀝀􀝀􀝔 (􀝔 􀯡 ) = 􀝊􀝔􀯡−1 |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  􀝀 \u003Cbr>􀝀􀝔 |  |  |  | (sin 􀝔 ) = cos |  |  |  | 􀝔 |\n|  􀝀 \u003Cbr>􀝀􀝔 |  |  | (cos 􀝔) = − sin 􀝔 |  |  |  |  |  |\n| 􀝀􀝀􀝔 (tan 􀝔) = sec2 􀝔􀝀􀝀􀝔 (cot 􀝔) = − csc2 􀝔 |  |  |  |  |  |  |  |  |\n|  􀝀 \u003Cbr>􀝀􀝔 |  | (sec 􀝔) = sec 􀝔 tan 􀝔 |  |  |  |  |  |  |\n|  􀝀 \u003Cbr>􀝀􀝔 | (csc 􀝔) = − csc 􀝔 cot 􀝔 |  |  |  |  |  |  |  |\n|  |  􀝀 \u003Cbr>􀝀􀝔 |  |  |  | (ln 􀝑) = | 1 􀝀􀝑\u003Cbr>􀝑 􀝀􀝔 |  |  |\n|  􀝀 \u003Cbr>􀝀􀝔 |  |  |  |  | (􀝁 􀯨 ) = 􀝁 􀯨 |  | 􀝀􀝑\u003Cbr>􀝀􀝔 |  |\n| Where u is a function of x, and a is a constant. |  |  |  |  |  |  |  |  |\n\nDifferentiation Rules Chain Rule:  \n􀯗􀯗􀯫 [􀝂 (􀝑)] = 􀝂 ′(􀝑) 􀯗􀯗􀯨􀯫 OR 􀯗􀯗􀯬􀯫 = 􀯗􀯗􀯬􀯨 􀯗􀯗􀯨􀯫  \nProduct Rule:  \n􀯗􀯗􀯫 (􀝑􀝒) = 􀝑 􀯗􀯗􀯩􀯫 + 􀝒 􀯗􀯗􀯨􀯫 OR 􀝑 􀝒 ′ + 􀝒 􀝑 ′  \nQuotient Rule:  \n􀯗􀯗􀯫 􁉀􀯨􀯩􁉁 = 􀯩~~ ~~􀳏􀳏2􀯨􀳏􀳏􀳡􀳣 OR 􀯩~~ ~~􀯨′2􀯨~~ ~~􀯩~~ ~~′  \nIntermediate Value Theorem  \nIf the function 􀝂(􀝔) is continuous on [􀜽, 􀜾], andy is a number between 􀝂(􀜽) and 􀝂(􀜾), then there exists at least one number 􀝔 = 􀜿 in the open interval (􀜽, 􀜾)  \nsuch that 􀝂(􀜿) = 􀝕 .  \nMean Value Theorem  \nIf the function 􀝂(􀝔) is continuous on [􀜽, 􀜾], AND the first derivative exists on the interval (􀜽, 􀜾) then thereis at least one number 􀝔 = 􀜿 in (􀜽, 􀜾) such that 􀝂 ′(􀜿) = 􀯙~~ ~~(􀯕􀯕)−􀯙􀯔(􀯔) .  \nRolle’s Theorem  \nIf the function 􀝂(􀝔) is continuous on [􀜽, 􀜾], AND the first derivative exists on the interval (􀜽, 􀜾) AND 􀝂 (􀜽) = 􀝂 (􀜾), then there is at least one number 􀝔 = 􀜿 in (􀜽, 􀜾) such that 􀝂 ′(􀜿) = 0 .  \n\n| Extreme Value Theorem |  |\n| --- | --- |\n| If the function 􀝂(􀝔) is continuous on [􀜽, 􀜾], then the function is guaranteed to have an absolute maximum\u003Cbr>and an absolute minimum on the interval. | |\n\nCurve Sketching And Analysis  \n􀝕 = 􀝂 (􀝔) must be continuous at each:  \nCritical point: 􀯗􀯗􀯬􀯫 = 0 or undefined LOOK OUT FOR ENDPOINTS  \nLocal minimum:  \n􀯗􀯗􀯬􀯫 goes (−, 0, +) or (−, 􀝑􀝊􀝀, +) OR ~~ ~~􀯗􀯗2􀯫􀯬2 > 0  \nLocal maximum:  \n􀯗􀯗􀯬􀯫 goes (+, 0, −) or (+, 􀝑􀝊􀝀 , −) OR ~~ ~~􀯗􀯗2􀯫􀯬2 \u003C 0  \nPoint of inflection: concavity changes  \n􀯗􀯗2􀯫􀯬2 goes from (+, 0, −),(−, 0, +), (+, 􀝑􀝊􀝀 , −), OR (−, 􀝑􀝊􀝀 , +)  \nDerivative of an Inverse Function:  \nIff has an inverse function g then:  \n􀝃 ′(􀝔) = 􀝂~~ ~~′(􀝃1(􀝔))  \nderivatives are reciprocal slopes  \nImplicit Differentiation  \nRemember that in implicit differentiation you will have a 􀯗􀯗􀯬􀯫 for each y in the original function or equation. Isolate the 􀯗􀯗􀯬􀯫~~ ~~ . If you are taking the second derivative 􀯗􀯗2􀯫􀯬2 , you will often substitute the expression you found for the first derivative somewhere in the process.  \n\n| Average Rate of Change ARoC: |  |\n| --- | --- |\n| 􀝉􀯦􀯘􀯖 = | 􀝂 (􀜾) − 􀝂 (􀜽)\u003Cbr>􀜾 − 􀜽 |\n\nInstantaneous Rate of Change IRoC:  \n􀝉􀯧􀯔􀯡 = 􀝂 ′(􀝔) = lim 􀝂 (􀝔 + ℎ) − 􀝂 (􀝔)  \nℎ→0 ℎ  \nWrite the equation of a tangent line at a poin","cbCaipsoBllljs17","https://ap.wps.com/l/cbCaipsoBllljs17","pdf",1730669,"English","# Alternate Definition of the Derivative\n# Basic Derivatives\n# Differentiation Rules\n# Key Calculus Theorems\n# Curve Sketching and Analysis\n# Inverse Functions and Implicit Differentiation\n# Average and Instantaneous Rate of Change\n# Tangent Lines and Extrema Tests\n# Asymptotes\n# Calculator Use Reminders\n# Logarithms and Exponential Growth/Decay","[{\"question\":\"What calculus theorems are included in this AP Calculus AB review?\",\"answer\":\"The review includes the Intermediate Value Theorem, Mean Value Theorem, Rolle’s Theorem, and the Extreme Value Theorem. Each is stated with the conditions needed on continuity and derivatives.\"},{\"question\":\"Which differentiation rules and derivative facts are summarized?\",\"answer\":\"It lists the chain rule, product rule, and quotient rule, along with an alternate definition of the derivative and a set of basic derivative formulas for standard functions.\"},{\"question\":\"How does the document guide curve sketching and finding maxima/minima?\",\"answer\":\"It instructs how to use critical points and endpoints, the sign changes of the first derivative for relative extrema, and the second derivative for concavity and inflection points. It also includes horizontal asymptote rules and tangent line setup.\"}]","Stuff You Must Know Cold - Exam Prep - AP Calculus AB | PDF"]