PDF-How to find ABSOLUTE extrema of a function on a closed intervel

STEP I Find the critical numbers of the function say that are in the interval ab STEP II Evaluate the function at the critical numbers That is calculate STEP III Evaluate the function at each endpoint of ab That is calculate and STEP IV The. Check hourslibrarycolumbiaedu for library hour updates Reserve a Group Study room roomreservationsculcolumbiaedu Unattended materials may be relocated given to the security guard or turned in to Lost Found Lost Found locations Circulation Office 3 Broad St Orange CT 06477 Wallingford CT 06492 203 799 0431 203 793 7722 Mon Sat 10am 7pm Mon Fri 10am 630pm Sunday Closed Sat 10am 5pm Sunday Closed Close for Lunch 130pm 2pm 3277 Berlin Turnpike 1115 New Britain Ave Newington CT 06111 West Hartfor Definition. A sentence part describing the rest of a sentence. An absolute phrase is ALMOST a complete sentence. . Modifies a whole clause or sentence, not just one word. Consists of a noun or noun equivalent + a participial phrase. Section 4.1. Definition of . Extrema. – . Let be defined on a interval. . containing :. . i. . is the minimum of on . . if . ii. is . 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.. Section 4.2a. Definition: Increasing/Decreasing Functions. A function that is always increasing or decreasing . on. a . particular . interval is . monotonic. on that interval. Let be . a function defined on an interval. If y varies directly as the square of x and inversely as z and y =36 when x =12 and z =8, find x when y=4, and z=32. 3.6 – Critical Points & Extrema. Objective: . Critical Points. Critical Points. 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. Ruler with absolute (total) power. . Doesn’t have to consult with nobles. Common people, or their representatives. . Who told you . you. could do that???. Divine Right of Kings. In these monarchies, the absolute rulers believed that they received their power from God and therefore, should not be challenged!. Students will be able to use integers to represent the velocity and the speed of an object as evidenced by . the class discussion after watching a short video.. https://www.youtube.com/watch?v=M9NBZJR5tyo. 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 . 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. 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. . Vocabulary. Absolute Value Function: f(x) = |x|. Vertex: highest or lowest point on the graph of an absolute value function.. Transformation: changes graph size, shape, position, or orientation.. Translation: is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, .