PPT-First Derivative Test, Concavity,

Points of Inflection Section 43a Writing True or False A critical point of a function always signifies an extreme value of the function Explain FALSE Counterexample. We have that AA 1 that is that the product of AA is the sum of the outer products of the columns of To see this consider that AA ij 1 pi pj because the ij element is the th row of which is the vector a a ni dotted with the th column of which is 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 Section 3.1b. Remember, that in . graphical terms. , the derivative of a. function at a given point can be thought of as the . slope. of the curve at that point…. Therefore, we can get a good idea of what the graph of. Vocabulary Test #1. Solicitous. Induce. Loathsome. Disdain. Pedantry. Derivative. Esteem. Collaborate. . TotS. Vocab Test #2. w. anton. b. alm. d. ulcet. s. ubmissive. r. everence. h. usbanded. w. arrant . 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). FGFOA Conference, Orlando FL,. Mark A. White, CPA, Partner, Purvis Gray & Company LLP. Jim Towne, Senior VP, DerivActiv. 1. Statement 53. Accounting and Financial Reporting for Derivative Instruments. VALUE THEOREMS. Derivability of a function :. A function . f . defined on [. a, b. ] is said to be derivable or differentiable at if exists. This limit is called derivative of . 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. 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 . 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 . Slope of the Tangent Line. If . f. is defined on an open interval containing . c. and the limit exists, then . . and the line through (. c. , . f. (. c. )) with slope . m. is the line tangent to the graph of . 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.