Explanation Provide the steps to find the absolute extrema of a continuous function as follows: Find the first derivative of the function and find the critical points using the relation y ′ = 0 . Neglect the critical numbers which is not in the interval [ a , b ] . Calculate the value of the function at all critical points and end points. Take the largest value as absolute maximum and and the smallest value as absolute minimum. Example: Consider the function y = x 3 + 6 x 2 + 9 x on [ − 2 , 1 ] . Provide the function as shown below. y = x 3 + 6 x 2 + 9 x (1) Differentiate equation (1) with respect to x . y ′ = 3 x 2 + 12 x + 9 = 3 ( x 2 + 4 x + 3 ) = 3 ( x + 1 ) ( x + 3 ) (2) The critical points occurs at a point where y ′ = 0 . Calculate the critical points as shown below. 3 ( x + 1 ) ( x + 3 ) = 0 x + 1 = 0 or x + 3 = 0 x = − 1 or x = − 3 Omit the critical point x = − 3

University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)

3rd Edition

ISBN: 9780321999573

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Explain how to calculate the absolute extrema of a continuous function on a closed interval with example.

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University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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