PPT-4.1 – Extreme Values of Functions

Extreme Values of a function are created when the function changes from increasing to decreasing or from decreasing to increasing Extreme value decreasing increasing increasing Extreme value decreasing. Extreme Values and The First Derivative Test Recall that a function is increasing on an interval if the increase in values implies an increase in values for all values from that interval x Analogously is decreasing if f These concepts completely c BSRLM discussion. March 12. th. 2011. Institute of Education. Why equations, graphs and functions. What’s the same and what’s different?. Equations. A=1/2bh . v. 2. - u. 2. = 2as . y = 2x+5 . 3x - 5=9 - 2x . 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. 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). Extreme Values of Functions. Find the extreme values . of:. Do Now. First, check the graph .  What does it suggest?. What is the . domain. of the function?. Since there are no endpoints, all extreme values must occur. David Plaxco. Linear Independence of Functions. Definition of linear independence of vector-valued functions. :. Let . f. i. : . I . = (. a,b. ) . → . . . n. , . I = 1, 2. ,…. , n. .. . The . Efficient Algorithms for Low-Sensitivity Functions. Rocco Servedio. Joint work with . Parikshit. . Gopalan. (MSR). Noam Nisan (MSR / Hebrew University). Kunal. . Talwar. (Google). Avi. . Wigderson. MEI. Anne Watson. 2017. Functions are a unifying idea in mathematics . For whom? . Understanding the functions concept. Representations. Covariation. e.g. instantaneous rate of change; constant and varying rates of change; sequential step sizes. 4. 3. 2. 1. 0. In addition to level 3.0 and beyond what was taught in class, the student may: . Make connection with other concepts in math.. Make connection with other content areas..  . The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables.. Notation. Functions on binary / returning binary values. Finite automaton model. We haven’t completely left the world of counting. Sometimes we wish to know how many functions / how many inputs … . Mean value theorem. Theorem . 3. : Mean Value Theorem for Derivatives. :. If is continuous at every point of the closed interval [a, b] and differentiable at every point of its interior (a, b), then there is at least one point c in (a, b) at .  .  . 4.7 Forming Functions . from Verbal Descriptions. 1. Form a function from a verbal description.. 2. . Determine . the maximum and minimum values.. Objectives:. An important concern of mathematics is finding the minimum or maximum value of a function. . Instructor: Teaching Assistants:. Justin Hsia . Anupam. . Gupta, . Cheng Ni, Eugene . Oh, . Sam Wolfson, Sophie Tian, Teagan . Horkan. Satellites Are Reshaping How Traders Track Earthly Commodities. All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S Gordon. ISBN 978-0-88385-767-0. Functions in the Real World. What are the two variables? . Which one depends on which? .