PPT-Section 3.4 – Concavity and the Second Derivative Test

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 . 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 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???. 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 . To see if something is concave down or concave up we need to look at the first derivative. Second Derivative Test for Concavity xf EXAMPLE: Use the graph to indicate the interval e notice that the g Local Extrema. Definition of Local Extrema. Let . P. be a point in the domain of . f. . Then. f. has a . local maximum. at the point . P. 0. if . f. (. P. 0. ) . ≥ . f. (. P. ) for all points . Quotient Rule. Objective:. Students will be able to use the product and quotient rule to take the derivative of differentiable equations . Review: Definition of Derivative. The derivative of . f. at . 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. Power, Sum, and Difference Rules, Higher-Order Derivatives. The “Do Now”. Find the derivative of. Does this make sense graphically???. The “Do Now”. Find the derivative of. Let’s see some patterns so we can generalize. 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 . Unified compliance testing across federal agencies and how it can improve accessibility for PWD’s: helping project managers, vendors, and developers deliver compliant products. Today’s Presentation. 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.