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• Critical point
  A '''critical point''' of a [[function]] <math>f(x)</math> is a point <math>(k,f(k))</mat
  261 bytes (42 words) - 20:27, 23 April 2008

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• Scholastic Aptitude Test
  ...'SATI ''', or just simply "SAT," is a [[standardized test]] that tests the critical reasoning skills that are needed for success in college. The majority of s The test contains three sections: a math section, a writing section, and a critical reading section. 800 points can be earned in each section; a student can r
  908 bytes (146 words) - 14:44, 12 December 2023
• 1983 AIME Problems/Problem 9
  ...h> are relative minima by finding the derivatives at other points near the critical points, or by checking that the second derivative <math>f''(y)=8y^{-3}</mat
  4 KB (722 words) - 20:25, 14 January 2023
• Critical point
  A '''critical point''' of a [[function]] <math>f(x)</math> is a point <math>(k,f(k))</mat
  261 bytes (42 words) - 20:27, 23 April 2008
• Proofs of AM-GM
  ...f this function. We can do this simply using calculus. We need to find the critical points of <math>f(x)</math>, we can do that by finding <math>f'(x)</math> a Note that this is the only critical point of <math>f(x)</math>. We can confirm it is the maximum by finding it'
  12 KB (2,171 words) - 07:55, 11 May 2023
• 2008 AIME I Problems/Problem 14
  Solving, we obtain <math>x=27</math> as the critical value. Hence, <math>k</math> has the maximum value of <math>(2*27-27)/27^2
  8 KB (1,333 words) - 00:18, 1 February 2024
• Statistical mechanics
  ...significant change in its bulk behavior as this parameter increases past a critical point. ...s, there is a phase-transition in the kinds of graph that result. Once the critical probability has been passed, the random graphs will suddenly be "dominated"
  1 KB (208 words) - 22:56, 13 June 2008
• Broadcom MASTERS
  ...nd compete in team hands-on STEM challenges to demonstrate their skills in critical thinking, collaboration, communication and creativity. Visit student.societ
  694 bytes (88 words) - 09:45, 23 December 2016
• The Ross Program
  ...ematics. The central goal of the Ross Program is building a foundation for critical thinking, rather than just preparing students for proficiency in computatio
  3 KB (474 words) - 20:48, 28 May 2013
• CIA Undergraduate Scholar Program
  * 1500 SAT (1000 Math & Critical Reading, 500 Writing) or 21 ACT scores or higher (high school students)
  2 KB (228 words) - 11:04, 23 July 2010
• 2011 AIME I Problems/Problem 6
  ...ac{9}{8}</math> because the vertex determines the axis of symmetry and the critical value of the parabola. The least integer greater than <math>-\frac{9}{8}</m
  4 KB (661 words) - 01:18, 11 December 2023
• 2011 AIME II Problems/Problem 10
  ...EPF</math> not the side. To apply Ptolemy's theorem like solution 4, it is critical to know whether <math>OP</math> is the diagonal or side of quadrilateral. E
  11 KB (1,720 words) - 03:12, 18 December 2023
• Jugemu Jugemu Goko no Surikire Kaijarisuigyo no Suigyomatsu Unraimatsu Furaimatsu Ku Neru Tokoro ni Sumu Tokoro Yabura Koji no Bura Koji Paipo-paipo Paipo no ShuringanShuringan no Gurindai Gurindai no Ponpokopi no Ponpokona no Chokyumei no Chosuke.
  Edit: Critical alert! An unknown hacker has changed the status on duskstream's AoPS page.
  611 bytes (89 words) - 16:32, 12 July 2022
• 1950 AHSME Problems/Problem 41
  ...ivative of the function is <math>2a</math>; since <math>a > 0</math>, this critical point is a minimum. As in Solution 1, plug this value into the function to
  1 KB (219 words) - 13:43, 4 April 2024
• Project Math Minds
  ...e decisions based on the results - the types of analytical skills that are critical for success in today's ever-changing economic climate. These are the skills
  1 KB (166 words) - 18:33, 15 December 2015
• Rapid Rabbit Relays
  However, each mathlete cannot do another mathlete's problem, so it's critical that Role 1 gets his/her answer correct.
  931 bytes (153 words) - 17:05, 4 October 2012
• 2012 AMC 8 Problems/Problem 20
  ...<math>(5, 7, 9)</math> can be put on an interval that does not contain the critical point <math>x=-14</math>, a greater <math>x</math> implies a greater <math>
  4 KB (513 words) - 18:34, 20 January 2024
• 1962 AHSME Problems/Problem 37
  We make <math>A' = 0</math> and get the critical point <math>x = \frac{1}{2}</math>.
  4 KB (631 words) - 09:08, 13 April 2023
• Optimization
  ...mums are part of the critical points of the function. The x-values of the critical points can be found by taking the derivative of <math>f(x)</math> and setti
  2 KB (274 words) - 10:44, 8 April 2024
• LSU Math Circle Summer Program
  ...ver the course of the program, students develop problem-solving abilities, critical thinking skills, and logical reasoning through projects, games, and puzzles
  2 KB (233 words) - 11:03, 19 September 2023
• QuanTM Math Circle Summer Program
  ...ver the course of the program, students develop problem-solving abilities, critical-thinking skills, and logical reasoning through engaging activities, problem
  1,010 bytes (141 words) - 20:17, 26 March 2019

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