PDF-RELATIVE EXTREMA AND FIRST DERIVATIVE TEST

Prepared by Ingrid Stewart PhD College of Southern Nevada Please Send Questions and Comments to ingridstewartcsnedu Thank you Lets look at the graph of a quadratic function and some of its t. 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???. Common Core II – Day 2. Warm Ups. a) Factor to solve the equation x. 2. – 7x + 10 = 0. . b) Explain what the solutions tell you about the graph. . c. ) Using what you know about the quadratic function, draw a rough sketch.. 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). 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). constant. Indicate all extrema (max and min) 242)(xxxfincreasing, as we move from left to right if the graph is going uphill then it is increasing. Likewise if we move from left to 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 . Extrema. Maximum and Minimums. Critical Values. . . . Where the derivative is zero or the function does not exist.. Extrema. : . Let f be defined on the interval (. a,b. ) containing the point c.. Definition of Extrema. Let f be defined on an interval . I. containing c.. f(c) is the . minimum. of f on . I. if f(c)≤f(x) for all x in . I. .. f(c) is the . maximum. of f on . I. if f(c)≥f(x) for all x in . 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 . Optimization. Chapter 8.1. Extreme Points and Saddle Points. 8.1- Extreme Points and Saddle Points. The optimization techniques for functions with a single input variable readily generalize to multivariable functions. . Relative and Absolute Extrema Math 200 Week 6 - Friday Math 200 Goals Be able to use partial derivatives to find critical points (possible locations of maxima or minima). Know how to use the Second Partials Test for functions of two variables to determine whether a critical point is a