PPT-Concavity

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 . Extreme Values and The Second Derivative Test Consider the following two increasing functions While they are both increasing their concavity distinguishes them The 64257rst function is said to be concave up and the second to be concave down More gen Notation dx dx y 00 f 00 Thus dx dx dy dx Example Find the second derivatives of the following functions a 2 x y 00 2 b y 00 c 5 4 5 y 00 The 64257rst derivative gives information about whether a funct ion increases or decreases In fact A d Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! Test for Concavity The graph of a function is said to be concave Points of Inflection. Section 4.3a. Writing: True . or . False – A . critical point . of. a function always signifies . an . extreme. value . of the . function. Explain.. FALSE!!! – Counterexample???. Dr . jp,asst. . prof,ich,mch,kottayam. The manifestations of rickets are most . pronounced with . rapid bone . growth . particularly the distal radius and ulna, distal femur. , proximal . tibia, proximal . Techniques in Active Tectonic Study. Juni 20-Juli 2, 2013. Instruktur: Prof. J Ramon Arrowsmith (JRA). Dari Arizona State University (ASU) - US. Tempat Pelaksanaan: . Ruang Pangea, Laboratorium Gempabumi (LabEarth) – Puslit Geoteknologi LIPI dan Kuliah lapangan akan dilakukan disekitar Sesar Lembang, Jawa Barat.. We will learn about:. Concavity -Points of Inflection - The Second Derivative Test. Review. If a functions wants to switch from decreasing to increasing. or visa versa, what are its options of approach/attack! (There is only three options). Speaker: . Hao-Chung Cheng. Co-work:. . Min-. Hsiu. Hsieh. Date:. 01/09/2016. 1. 2. Discrete Memoryless Channel. n. -block encoder. Error probability: . Rate of the code: . Shannon’s theory: . n. FACULTY OF EDUCATION. Mathematics Education . Department. Concavity And The Second Derivative. 1. Orhan TUĞ (PhDc). Concavity. Concavity . State the signs of . and . on the interval (0,2)..  . Example 1. nd. Derivative Test. Objectives:. To find Higher Order Derivatives. To use the second derivative to test for concavity. To use the 2. nd. Derivative Test to find relative . extrema. If a function’s derivative is . The Second Derivative and the Function. The first derivative tells us where a function is increasing or decreasing. But how can we tell the manner in which a function is increasing or decreasing?. For example, if . Monotonicity – defines where a function is increasing or decreasing.. A function is monotonic if it is increasing or decreasing on an interval.. d. a. b. c.  . Monotonicity of . Interval. Increasing/Decreasing. . prof,ich,mch,kottayam. The manifestations of rickets are most . pronounced with . rapid bone . growth . particularly the distal radius and ulna, distal femur. , proximal . tibia, proximal . humerus. 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? .