PPT-Extrema on an Interval Section 3.1 AP Calculus

Definition of Extrema Let f be defined on an interval I containing c fc is the minimum of f on I if fcfx for all x in I fc is the maximum of f on I if fcfx for all x in . A Construction Using Fourier Approximations. UNIVERSALITY. To find one (or just a few) mathematical relationships (functions or equations) to describe a certain connection between ideas. .. Examples of this are common in science. Section 4.1. Definition of . Extrema. – . Let be defined on a interval. . containing :. . i. . is the minimum of on . . if . ii. is . Common Core II – Day 2. Warm Ups. a) Factor to solve the equation x. 2. – 7x + 10 = 0. . b) Explain what the solutions tell you about the graph. . c. ) Using what you know about the quadratic function, draw a rough sketch.. Ms. . Battaglia. – . ap. calculus . Definite integral. A definite integral is an integral . with upper and lower bounds. The number a is the . lower limit. of integration, and the number b is the . Chapter 5.1. Absolute (Global) Extreme Values. Up to now we have used the derivative in applications to find rates of change. However, we are not limited to the rate-of-change interpretation of the derivative. If y varies directly as the square of x and inversely as z and y =36 when x =12 and z =8, find x when y=4, and z=32. 3.6 – Critical Points & Extrema. Objective: . Critical Points. Critical Points. Why find extreme values of functions?. To find where functions are optimized. Find maximum profit. Find minimum cost. Find best dose of medicine. Find best gas mileage per speed. Etc….. Extrema. (plural of extreme). constant. Indicate all extrema (max and min) 242)(xxxfincreasing, as we move from left to right if the graph is going uphill then it is increasing. Likewise if we move from left to Extrema. Maximum and Minimums. Critical Values. . . . Where the derivative is zero or the function does not exist.. Extrema. : . Let f be defined on the interval (. a,b. ) containing the point c.. Applied Calculus ,4/E, Deborah Hughes-. Hallett. Copyright 2010 by John Wiley and Sons, All Rights Reserved. Applied Calculus ,4/E, Deborah Hughes-. Hallett. Copyright 2010 by John Wiley and Sons, All Rights Reserved. As the number of rectangles increased, the approximation of the area under the curve approaches a value.. Copyright .  2010 Pearson Education, Inc.. Section 5.3 – The Definite Integral. Definition. Recitation 14. (12/4/2012). TA: Zhen . (Alan) . Zhang. zhangz19@stt.msu.edu. Office hour: (C500 WH) 1:45 – 2:45PM . Tuesday. (office . tel.: . 432-3342). Help-room: (A102 WH) 11:20AM-12:30PM, . Monday, Friday. Books ordered. Stewart. . Calculus: Early . Transcendentals. 7e. Ocean. Ngl.cengage.com. Stewart. . Calculus: Early . Transcendentals. 7e. Middlesex. Ngl.cengage.com. Larson:. Calculus of a Single Variable: Early . C. CONVERSATION: Voice level 0. No talking!. H. HELP: Raise your hand and wait to be called on.. A. ACTIVITY: Whole class instruction; students in seats.. M. . MOVEMENT: Remain in seat during instruction..