Explanation The function is f ( x ) = 1 3 x 3 + 3 2 x 2 − 4 x + 1 and interval is [ − 5 , 2 ] . Find the critical number in the interval [ − 5 , 2 ] to compute the absolute minimum and absolute maximum. Differentiate the function f ( x ) = 1 3 x 3 + 3 2 x 2 − 4 x + 1 as follows, f ′ ( x ) = d d x ( 1 3 x 3 + 3 2 x 2 − 4 x + 1 ) = 1 3 ( 3 ) x 3 − 1 + 3 2 ( 2 ) x 2 − 1 − 4 + 0 = x 2 + 3 x − 4 = ( x + 4 ) ( x − 1 ) Set f ′ ( x ) = 0 and solve for x . That is, x + 4 = 0 or x − 1 = 0 . Hence, the critical numbers are x = − 4 and x = 1 . Here, it is observed that the points − 4 and 1 lies in the given interval [ − 5 , 2 ] . Find the values of the function at the critical points and the end points of the given interval. Substitute x = − 4 in f ( x ) = 1 3 x 3 + 3 2 x 2 − 4 x + 1 , f ( − 4 ) = 1 3 ( − 4 ) 3 + 3 2 ( − 4 ) 2 − 4 ( − 4 ) + 1 = 1 3 ( − 64 ) + 3 2 ( 16 ) + 16 + 1 = − 21.3333 + 24 + 16 + 1 ≈ 19 .67 That is, f ( − 4 ) ≈ 19 .67 . Substitute x = 1 in f ( x ) = 1 3 x 3 + 3 2 x 2 − 4 x + 1 , f ( 1 ) = 1 3 ( 1 ) 3 + 3 2 ( 1 ) 2 − 4 ( 1 ) + 1 = 1 3 + 3 2 − 4 + 1 = 0

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 14.1, Problem 13E

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To find: The absolute extrema of f(x)=13x3+32x2−4x+1 on the domain [−5,2] if exist and verify the answer using the graphing calculator.

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Chapter 14.1, Problem 12E

Chapter 14.1, Problem 14E

Chapter 14 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 14.1 - Find the absolute extrema of the function f(x) =...Ch. 14.1 - Find the locations and values of the absolute...Ch. 14.1 - Prob. 1WE Ch. 14.1 - Find all critical numbers for each of the...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Find the locations of any absolute extrema for the...Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E

Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E Ch. 14.1 - Prob. 11E Ch. 14.1 - Prob. 12E Ch. 14.1 - Prob. 13E Ch. 14.1 - Prob. 14E Ch. 14.1 - Prob. 15E Ch. 14.1 - Prob. 16E Ch. 14.1 - Find the absolute extrema if they exist, as well...Ch. 14.1 - Prob. 18E Ch. 14.1 - Prob. 19E Ch. 14.1 - Prob. 20E Ch. 14.1 - Prob. 21E Ch. 14.1 - Prob. 22E Ch. 14.1 - Prob. 23E Ch. 14.1 - Prob. 24E Ch. 14.1 - Prob. 25E Ch. 14.1 - Prob. 26E Ch. 14.1 - Prob. 27E Ch. 14.1 - Prob. 28E Ch. 14.1 - Prob. 29E Ch. 14.1 - Prob. 30E Ch. 14.1 - Prob. 31E Ch. 14.1 - Prob. 32E Ch. 14.1 - Prob. 33E Ch. 14.1 - Prob. 34E Ch. 14.1 - Prob. 35E Ch. 14.1 - Find the absolute extrema if they exist, as well...Ch. 14.1 - Prob. 37E Ch. 14.1 - Prob. 38E Ch. 14.1 - Prob. 39E Ch. 14.1 - Prob. 40E Ch. 14.1 - Prob. 41E Ch. 14.1 - Prob. 42E Ch. 14.1 - Prob. 43E Ch. 14.1 - Prob. 44E Ch. 14.1 - Prob. 45E Ch. 14.1 - Prob. 46E Ch. 14.1 - Prob. 47E Ch. 14.1 - Prob. 48E Ch. 14.1 - Prob. 49E Ch. 14.1 - Prob. 50E Ch. 14.1 - Prob. 51E Ch. 14.1 - Prob. 53E Ch. 14.1 - Salmon Spawning The number of salmon swimming...Ch. 14.1 - Prob. 55E Ch. 14.1 - Prob. 56E Ch. 14.1 - Prob. 57E Ch. 14.1 - Prob. 58E Ch. 14.1 - Prob. 59E Ch. 14.1 - Prob. 60E Ch. 14.1 - Prob. 61E Ch. 14.1 - Prob. 62E Ch. 14.2 - Prob. 1YT Ch. 14.2 - Prob. 2YT Ch. 14.2 - Prob. 3YT Ch. 14.2 - Prob. 4YT Ch. 14.2 - Prob. 1WE Ch. 14.2 - Prob. 2WE Ch. 14.2 - Prob. 1E Ch. 14.2 - Prob. 2E Ch. 14.2 - Prob. 3E Ch. 14.2 - Prob. 4E Ch. 14.2 - Prob. 5E Ch. 14.2 - Prob. 6E Ch. 14.2 - Prob. 7E Ch. 14.2 - Prob. 8E Ch. 14.2 - Prob. 9E Ch. 14.2 - Prob. 10E Ch. 14.2 - Prob. 11E Ch. 14.2 - Prob. 12E Ch. 14.2 - Prob. 13E Ch. 14.2 - Prob. 14E Ch. 14.2 - Revenue A local club is arranging a charter flight...Ch. 14.2 - Prob. 16E Ch. 14.2 - Prob. 17E Ch. 14.2 - Prob. 18E Ch. 14.2 - Prob. 19E Ch. 14.2 - Prob. 20E Ch. 14.2 - Prob. 21E Ch. 14.2 - Prob. 22E Ch. 14.2 - Prob. 23E Ch. 14.2 - Prob. 24E Ch. 14.2 - Prob. 25E Ch. 14.2 - Container Design Your company needs to design...Ch. 14.2 - 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Prob. 8E Ch. 14.3 - Prob. 9E Ch. 14.3 - Prob. 10E Ch. 14.3 - Prob. 11E Ch. 14.3 - Prob. 12E Ch. 14.3 - Prob. 13E Ch. 14.3 - Prob. 14E Ch. 14.3 - Prob. 15E Ch. 14.3 - Prob. 16E Ch. 14.3 - Prob. 17E Ch. 14.3 - Prob. 18E Ch. 14.3 - Elasticity For each of the following demand...Ch. 14.3 - Elasticity For each of the following demand...Ch. 14.3 - Prob. 21E Ch. 14.3 - Elasticity For each of the following demand...Ch. 14.3 - Prob. 23E Ch. 14.3 - Prob. 24E Ch. 14.3 - Prob. 25E Ch. 14.3 - Prob. 26E Ch. 14.3 - Prob. 27E Ch. 14.3 - Prob. 28E Ch. 14.3 - Elasticity of Software The Valve Corporation, a...Ch. 14.3 - Prob. 30E Ch. 14.3 - Elasticity A study of the demand for air travel in...Ch. 14.3 - Elasticity The price along the West Coast of the...Ch. 14.3 - Prob. 33E Ch. 14.3 - Prob. 34E Ch. 14.4 - Prob. 1YT Ch. 14.4 - Prob. 2YT Ch. 14.4 - The graph of y4 x4 y2 + x2 = 0 is called the...Ch. 14.4 - Prob. 4YT Ch. 14.4 - Prob. 1WE Ch. 14.4 - Prob. 2WE Ch. 14.4 - Find dy/dx by implicit differentiation for the...Ch. 14.4 - 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Prob. 49E Ch. 14.4 - Prob. 50E Ch. 14.4 - Prob. 51E Ch. 14.4 - Prob. 52E Ch. 14.4 - Prob. 53E Ch. 14.5 - Prob. 1YT Ch. 14.5 - Prob. 2YT Ch. 14.5 - Prob. 3YT Ch. 14.5 - Prob. 4YT Ch. 14.5 - Prob. 1WE Ch. 14.5 - Prob. 2WE Ch. 14.5 - Prob. 1E Ch. 14.5 - Prob. 2E Ch. 14.5 - Prob. 3E Ch. 14.5 - Prob. 4E Ch. 14.5 - Prob. 5E Ch. 14.5 - Prob. 6E Ch. 14.5 - Prob. 7E Ch. 14.5 - Prob. 8E Ch. 14.5 - Prob. 9E Ch. 14.5 - Prob. 10E Ch. 14.5 - Prob. 11E Ch. 14.5 - Prob. 12E Ch. 14.5 - Prob. 13E Ch. 14.5 - Prob. 14E Ch. 14.5 - Prob. 15E Ch. 14.5 - Prob. 16E Ch. 14.5 - Prob. 17E Ch. 14.5 - Prob. 18E Ch. 14.5 - Prob. 19E Ch. 14.5 - Prob. 20E Ch. 14.5 - Prob. 21E Ch. 14.5 - Prob. 22E Ch. 14.5 - Prob. 23E Ch. 14.5 - Prob. 24E Ch. 14.5 - Prob. 25E Ch. 14.5 - Prob. 26E Ch. 14.5 - Prob. 27E Ch. 14.5 - Prob. 28E Ch. 14.5 - Prob. 29E Ch. 14.5 - Prob. 30E Ch. 14.5 - Prob. 31E Ch. 14.5 - Prob. 32E Ch. 14.6 - Prob. 1YT Ch. 14.6 - Prob. 2YT Ch. 14.6 - Prob. 3YT Ch. 14.6 - Prob. 1WE Ch. 14.6 - Prob. 2WE Ch. 14.6 - Prob. 1E Ch. 14.6 - Prob. 2E Ch. 14.6 - Prob. 3E Ch. 14.6 - Prob. 4E Ch. 14.6 - Prob. 5E Ch. 14.6 - For Exercises 18, find dy for the given values of...Ch. 14.6 - For Exercises 18, find dy for the given values of...Ch. 14.6 - Prob. 8E Ch. 14.6 - Prob. 9E Ch. 14.6 - Prob. 10E Ch. 14.6 - Prob. 11E Ch. 14.6 - Prob. 12E Ch. 14.6 - Prob. 13E Ch. 14.6 - Prob. 14E Ch. 14.6 - Use the differential to approximate each quantity....Ch. 14.6 - Prob. 16E Ch. 14.6 - Business and Economies 17.Demand The demand for...Ch. 14.6 - Prob. 18E Ch. 14.6 - Revenue A company estimates that the revenue (in...Ch. 14.6 - Prob. 20E Ch. 14.6 - Prob. 21E Ch. 14.6 - Prob. 22E Ch. 14.6 - Prob. 23E Ch. 14.6 - Prob. 24E Ch. 14.6 - Prob. 25E Ch. 14.6 - Prob. 26E Ch. 14.6 - Prob. 27E Ch. 14.6 - Prob. 28E Ch. 14.6 - Prob. 29E Ch. 14.6 - Gray Wolves Accurate methods of estimating the age...Ch. 14.6 - Prob. 31E Ch. 14.6 - Prob. 32E Ch. 14.6 - Prob. 33E Ch. 14.6 - Prob. 34E Ch. 14.6 - Prob. 35E Ch. 14.6 - Prob. 36E Ch. 14.6 - Prob. 37E Ch. 14.6 - Prob. 38E Ch. 14.6 - Prob. 39E Ch. 14.6 - Prob. 40E Ch. 14.6 - Prob. 41E Ch. 14 - The absolute maximum of a function always occurs...Ch. 14 - A continuous function on a closed interval has an...Ch. 14 - Prob. 3RE Ch. 14 - Prob. 4RE Ch. 14 - Total revenue is maximized at the price where...Ch. 14 - Prob. 6RE Ch. 14 - Prob. 7RE Ch. 14 - Prob. 8RE Ch. 14 - Prob. 9RE Ch. 14 - Prob. 10RE Ch. 14 - Prob. 11RE Ch. 14 - Prob. 12RE Ch. 14 - Prob. 13RE Ch. 14 - Prob. 14RE Ch. 14 - Prob. 15RE Ch. 14 - Prob. 16RE Ch. 14 - Prob. 17RE Ch. 14 - Prob. 18RE Ch. 14 - Prob. 19RE Ch. 14 - Prob. 20RE Ch. 14 - Prob. 21RE Ch. 14 - Prob. 22RE Ch. 14 - Prob. 23RE Ch. 14 - Prob. 24RE Ch. 14 - Prob. 25RE Ch. 14 - Prob. 26RE Ch. 14 - Prob. 27RE Ch. 14 - Prob. 28RE Ch. 14 - Prob. 29RE Ch. 14 - Prob. 30RE Ch. 14 - Prob. 31RE Ch. 14 - Why is implicit differentiation used in related...Ch. 14 - Prob. 33RE Ch. 14 - Prob. 34RE Ch. 14 - Prob. 35RE Ch. 14 - Prob. 36RE Ch. 14 - Prob. 37RE Ch. 14 - Prob. 38RE Ch. 14 - Prob. 39RE Ch. 14 - Prob. 40RE Ch. 14 - Prob. 41RE Ch. 14 - Prob. 42RE Ch. 14 - Prob. 43RE Ch. 14 - Prob. 44RE Ch. 14 - Prob. 45RE Ch. 14 - Prob. 46RE Ch. 14 - Prob. 47RE Ch. 14 - Prob. 48RE Ch. 14 - Prob. 49RE Ch. 14 - Prob. 50RE Ch. 14 - Prob. 51RE Ch. 14 - Prob. 52RE Ch. 14 - Prob. 53RE Ch. 14 - Prob. 54RE Ch. 14 - Prob. 55RE Ch. 14 - Prob. 56RE Ch. 14 - Prob. 57RE Ch. 14 - Prob. 58RE Ch. 14 - Prob. 59RE Ch. 14 - Prob. 60RE Ch. 14 - Prob. 61RE Ch. 14 - Prob. 62RE Ch. 14 - Prob. 63RE Ch. 14 - Prob. 64RE Ch. 14 - Prob. 65RE Ch. 14 - Prob. 66RE Ch. 14 - Prob. 67RE Ch. 14 - Prob. 68RE

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The absolute extrema of f ( x ) = 1 3 x 3 + 3 2 x 2 − 4 x + 1 on the domain [ − 5 , 2 ] if exist and verify the answer using the graphing calculator.

Solution Summary: The author explains how to find the absolute extrema of f(x)=13x

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To find: The absolute extrema of f(x)=13x3+32x2−4x+1 on the domain [−5,2] if exist and verify the answer using the graphing calculator.

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Chapter 14 Solutions