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 . adding it all up. Integral Calculus. 1. Goal. Compute the . signed. area . under some portion of an arbitrary curve. Integral Calculus. 2. Divide and Conquer. Integral Calculus. 3. Animatedly. Integral Calculus. A Service Learning Experience. Melinda Rudibaugh. Mathematics Faculty,. Chandler-Gilbert Community College. What is Service Learning?. Not volunteerism. Tied to the curriculum. Requires meaningful reflection and self-growth. 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 . How . do you know . how fast. You are going? . “well . how do you know. How fast you’re going. Right now,. At this very second?” . Push your friend so . that his/her . speed . changes. Try . AC 2311 C ** Calculus I ( 4 ) AC 2312 ** Calculus II ( 4 ) AC 2313 ** ( 4 ) HY 2048 C ** Physics for Engineers I ( 4 ) HY 2049 C ** Physics for Engineers II ( 4 ) AP 2302 ** Differential 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. 8. Newton & Leibniz. History & Philosophy of Calculus, Session . 8. The invention of the calculus. Newton and Leibniz in 17. th. Century invented the algorithmic procedures underlying the calculus. Newton & Leibniz. Summary. Calculus seems to demand some concept of the infinitesimal. Magnitude. New number. Or both?. But infinitesimals lack . clarity . Concepts that are not mathematical being used to interpret mathematics?. The Return of the Infinitesimal?. So far on this course we’ve stayed close to mainstream mathematics.. In this final session we look at some more “fancy” material, much of it very recent.. These aren’t just techniques for doing complicated calculations – they represent new ways to think about geometry and continuity, and so they promise to raise some old philosophical questions. . Intervals Increasing. Intervals Decreasing. Intervals Concave Up. Intervals Concave Down. Critical Numbers:. Relative . Extrema. :. Points of Inflections:. Make a table to find intervals of concavity . The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Calculus. The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Section 1.1. Functions and Change. Calculus, 7th edition, Hughes-Hallett et.al., Copyright 2017 by John Wiley & Sons, All Rights Reserved. Definition of a Function. A . function . is a rule that takes certain numbers as inputs and assigns to each a definite output number. The set of all input numbers is called the . 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 . YangQuan Chen, Ph.D., Director, . MESA . (Mechatronics, Embedded Systems and Automation). Lab. MEAM/EECS, School of Engineering,. University of California, Merced. E. : . yqchen@ieee.org. ; . or. , yangquan.chen@ucmerced.edu.