https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/a/analytical-applications-of-differentiation-frqs 2026-06-25T15:40:55.094699315Z Analytical applications of differentiation FRQs What types of questions focus on concepts from this unit? What makes a high-quality response? How are the responses scored? This article walks you through these questions. article https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2011-calculus-ab-free-response-4d 2026-06-29T20:40:47.259641521Z Using the Mean Value Theorem: 2011 Calculus AB free response #4d Mean Value Theorem and differentiability Sal Khan video https://cdn.kastatic.org/googleusercontent/sxxUyTFC78Tk_o3fD0SKyZMvcjIfAAzHieu0G4wj7z3PX2Hff-t-4wF3eWlb4TC2-SdNcZAWJ1AnHBUMWfmZd3r- Using the Mean Value Theorem: 2011 Calculus AB free response #4d Mean Value Theorem and differentiability https://cdn.kastatic.org/ka-youtube-converted/yX3JpmEgNHo.mp4/yX3JpmEgNHo.mp4 346 Free response questions: analytical applications of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2015-ap-calculus-ab-5-a 2026-06-29T20:40:47.259641521Z Finding relative maximum: 2015 AP Calculus AB 5a Maxima for f from graph of f' video https://cdn.kastatic.org/googleusercontent/Oi6xstmYVfOSSjLIKaeKiXqIo34_ylabaICITOaz6MnOL7N4EW_2dRDjqTtOWcV66U3EeuwwcD8YEe8-IfOQnko5 Finding relative maximum: 2015 AP Calculus AB 5a Maxima for f from graph of f' https://cdn.kastatic.org/ka-youtube-converted/j_kI7OcaLKI.mp4/j_kI7OcaLKI.mp4 275 Free response questions: analytical applications of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2015-ap-calculus-ab-5b 2026-06-29T20:40:47.259641521Z Analyzing function features: 2015 AP Calculus AB 5b Intervals where f is concave downwards and decreasing. video https://cdn.kastatic.org/googleusercontent/5DKkvR9HJpIxX4mJRHeSzhuifIws7MAQy7BLee8jDY29caPvbgCNzlcRRvclvGCd5KMpWFfMMb4f5c8Z8_Z9V-g Analyzing function features: 2015 AP Calculus AB 5b Intervals where f is concave downwards and decreasing. https://cdn.kastatic.org/ka-youtube-converted/bba11I93w8o.mp4/bba11I93w8o.mp4 181 Free response questions: analytical applications of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2015-ap-calculus-ab-5c 2026-06-29T20:40:47.259641521Z Finding inflection points: 2015 AP Calculus AB 5c Inflection points for a function video https://cdn.kastatic.org/googleusercontent/93_bX7V9LqWg26riTO2SxFOR7j7iymFaHmGjW2bkcdBVacRp-57AmzqXW-k85ijIYXmLcFv-ssuh8KK001612Xur Finding inflection points: 2015 AP Calculus AB 5c Inflection points for a function https://cdn.kastatic.org/ka-youtube-converted/ol4bW-3qs_s.mp4/ol4bW-3qs_s.mp4 196 Free response questions: analytical applications of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2015-ap-calculus-ab-6b 2026-06-29T20:40:47.259641521Z Finding vertical tangent lines: 2015 AP Calculus AB 6b Point on curve where tangent is vertical video https://cdn.kastatic.org/googleusercontent/NOfab4SG-qNEYkJ8mC3JpzPtQ9M74nCITdDO0QTQFXgM4l9F_90-3y6B-uZ0vfPWt-51BT4gxPgwu9DhgeHoAlP6 Finding vertical tangent lines: 2015 AP Calculus AB 6b Point on curve where tangent is vertical https://cdn.kastatic.org/ka-youtube-converted/s3jvXHQlO-c.mp4/s3jvXHQlO-c.mp4 282 Free response questions: analytical applications of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/x2dd7feea:analytical-applications-of-differentiation-free-response-questions/v/2017-ap-calculus-abbc-4b 2026-06-29T20:40:47.259641521Z Using concavity for reasoning: 2017 AP Calculus AB/BC 4b Potato problem from 2017 AP exam (Question 4, part b). Taking the second derivative using the chain rule to think about concavity. video https://cdn.kastatic.org/ka_thumbnails_cache/5f7f5430-e9f1-45a2-a2d3-df72969e5df8_1280_720_base.png Using concavity for reasoning: 2017 AP Calculus AB/BC 4b Potato problem from 2017 AP exam (Question 4, part b). Taking the second derivative using the chain rule to think about concavity. https://cdn.kastatic.org/ka-youtube-converted/OzhjlMnQ114.mp4/OzhjlMnQ114.mp4 312 Free response questions: analytical applications of differentiation