Critical Points & Local Extrema Math 126 past exam problems
65 past University of Washington exam problems on Critical Points & Local Extrema (textbook section 14.7), usually tested on the Midterm 2 and Final exams.
Skills tested most
Critical points · Second derivative test · Volume · Critical Points & Local Extrema · Double integrals · Quadric surfaces · Planes · Surfaces
Every past Critical Points & Local Extrema problem
- Midterm 2, Spring 2026 · Problem 2 · LovelessSecond derivative test, Setting up double integrals
- Midterm 2, Spring 2026 · Problem 4 · LovelessOptimization with a constraint
- Midterm 2, Spring 2025 · Problem 2 · LovelessCritical points, Second derivative test, Quadric surfaces
- Midterm 2, Spring 2025 · Problem 2 · CamachoSecond derivative test
- Final, Spring 2025 · Problem 4 · Camacho, Loveless, OstroffVolume, Planes
- Midterm 2, Autumn 2024 · Problem 2 · BekyelVolume, Quadric surfaces
- Final, Autumn 2024 · Problem 4 · Bekyel, Camacho, OstroffCritical points
- Final, Spring 2024 · Problem 4 · Yuan, Loveless, OstroffVolume
- Midterm 2, Winter 2024 · Problem 2 · LovelessCritical points, Second derivative test
- Midterm 2, Winter 2024 · Problem 3 · LovelessVolume
- Final, Winter 2024 · Problem 4 · Su, Loveless, Bekyel, OstroffSurfaces
- Final, Winter 2024 · Problem 5 · Su, Loveless, Bekyel, OstroffLines and planes, Double integrals, Functions of several variables
- Final, Winter 2024 · Problem 6 · Su, Loveless, Bekyel, OstroffVolume, Quadric surfaces
- Midterm 2, Autumn 2023 · Problem 1 · OstroffCritical points, Second derivative test
- Midterm 2, Autumn 2023 · Problem 1 · SuCritical points, Second derivative test
- Final, Autumn 2023 · Problem 4 · Su, Zhang, OstroffVolume, Planes
- Midterm 1, Spring 2023 · Problem 1 · LovelessDot product
- Midterm 1, Spring 2023 · Problem 3 · LovelessArc length
- Midterm 2, Spring 2023 · Problem 2 · LovelessCritical points, Second derivative test, Changing the order of integration
- Midterm 2, Spring 2023 · Problem 4 · LovelessVolume, Critical points, Second derivative test
- Final, Spring 2023 · Problem 3 · Loveless, Su, OstroffSecond derivative test, Tangent planes, Planes
- Final, Spring 2023 · Problem 6 · Loveless, Su, OstroffCritical Points & Local Extrema
- Final, Winter 2023 · Problem 6 · Drouot, Su, ZhangDouble integrals
- Final, Autumn 2022 · Problem 3 · Su, Nichifor, ZhuCritical points, Absolute extrema
- Final, Autumn 2022 · Problem 6 · Su, Nichifor, ZhuDouble integrals
- Final, Winter 2022 · Problem 3 · Ostroff, ZhangSurfaces
- Midterm 2, Autumn 2021 · Problem 2 · SuCritical points, Second derivative test
- Midterm 2, Autumn 2021 · Problem 3 · OstroffCritical points, Second derivative test
- Final, Autumn 2021 · Problem 3 · Su, OstroffCritical points, Absolute extrema
- Final, Autumn 2021 · Problem 4 · Su, OstroffCritical Points & Local Extrema
- Final, Autumn 2021 · Problem 5 · Su, OstroffDouble integrals
- Midterm 2, Spring 2019 · Problem 2 · LovelessCritical points
- Midterm 2, Spring 2019 · Problem 3 · OstroffQuadric surfaces
- Midterm 2, Spring 2019 · Problem 4 · LovelessAbsolute extrema, Critical points
- Final, Spring 2019 · Problem 2 · Athreya, Loveless, Pal, Conroy, OstroffLines in space, Planes, Dot product
- Midterm 2, Winter 2019 · Problem 2 · AthreyaCritical points
- Midterm 2, Winter 2019 · Problem 3 · TaggartCritical points
- Midterm 2, Winter 2019 · Problem 5 · AthreyaQuadric surfaces, Critical points
- Midterm 2, Winter 2019 · Problem 6 · OstroffCritical points
- Final, Winter 2019 · Problem 4 · Athreya, Burke, Taggart, OstroffCritical points
- Midterm 2, Autumn 2018 · Problem 4 · LovelessVolume, Planes, Critical points
- Midterm 1, Spring 2018 · Problem 1 · LovelessDot product
- Midterm 2, Spring 2018 · Problem 2 · LovelessCritical points, Second derivative test
- Final, Spring 2018 · Problem 6 · Bekyel, Loveless, ZhangVolume
- Final, Winter 2018 · Problem 6 · Burke, Taggart, PalCritical Points & Local Extrema
- Final, Autumn 2017 · Problem 3 · Athreya, Zhang, Taggart, OstroffCritical points
- Final, Autumn 2017 · Problem 5 · Athreya, Zhang, Taggart, OstroffDouble integrals
- Midterm 2, Spring 2017 · Problem 3 · LovelessCritical points, Second derivative test, Changing the order of integration
- Midterm 2, Spring 2017 · Problem 4 · LovelessVolume, Polar coordinates
- Final, Spring 2017 · Problem 4 · Loveless, Zhang, TaggartSurfaces
- Final, Spring 2017 · Problem 7 · Loveless, Zhang, TaggartDouble integrals
- Final, Winter 2017 · Problem 1 · Yuan, Zhang, LieblichSurfaces
- Final, Winter 2017 · Problem 2 · Yuan, Zhang, LieblichPolar coordinates
- Final, Winter 2017 · Problem 5 · Yuan, Zhang, LieblichQuadric surfaces
- Midterm 1, Winter 2016 · Problem 4 · LovelessLines and planes
- Midterm 2, Winter 2016 · Problem 2 · LovelessCritical points, Second derivative test
- Midterm 2, Winter 2015 · Problem 4 · LovelessCritical points
- Midterm 2, Autumn 2013 · Problem 4 · LovelessVolume
- Midterm 2, Spring 2013 · Problem 4 · LovelessCritical Points & Local Extrema
- Midterm 2, Spring 2012 · Problem 3 · LovelessCritical points
- Midterm 2, Spring 2011 · Problem 2 · LovelessPartial derivatives, Critical points
- Midterm 2, Spring 2010 · Problem 5 · LovelessCritical Points & Local Extrema
- Midterm 2, Spring 2008 · Problem 5 · ConroyCritical points
- Final, Spring 2008 · Problem 9 · Zhang, Bekyel, TaggartOptimization
- Final, Spring 2007 · Problem 9 · MilakisCritical Points & Local Extrema