Explanation Given: An algebraic function is; f ( x , y ) = 4 x 3 y 2 − 4 x y Formula used: The formula of derivative is; d d x ( x n ) = n x n − 1 Calculation: Consider the function: f ( x , y ) = 4 x 3 y 2 − 4 x y Take second order partial derivative of the function with respect to x as mentioned below, f x = ∂ ∂ x ( 4 x 3 y 2 − 4 x y ) = 12 x 2 y 2 − 4 y Further, differentiate partially with respect to x as; f x x = ∂ ∂ x ( f x ) = ∂ ∂ x ( 12 x 2 y 2 − 4 y ) f x x = 24 x y 2 Now calculate first order partial derivative of the function with respect to x and then calculate the second order partial derivative with respect to y

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 14, Problem 27RE

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To Calculate: The second order derivatives (fxx,fxy) of the function f(x,y)=4x3y2−4xy.

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Chapter 14, Problem 26RE

Chapter 14, Problem 28RE

Chapter 14 Solutions

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Ch. 14.1 - Prob. 1CP Ch. 14.1 - Prob. 2CP Ch. 14.1 - Prob. 3CP Ch. 14.1 - Prob. 4CP Ch. 14.1 - Prob. 5CP Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E 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 - Prob. 17E 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. 33E Ch. 14.1 - Prob. 34E Ch. 14.1 - Prob. 31E Ch. 14.1 - Prob. 32E Ch. 14.1 - Prob. 38E Ch. 14.1 - Prob. 35E Ch. 14.1 - Prob. 36E Ch. 14.1 - Prob. 37E Ch. 14.1 - Work these exercises. Checkout Lines According to...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. 14.2 - Prob. 1CP Ch. 14.2 - Prob. 2CP Ch. 14.2 - Prob. 3CP Ch. 14.2 - Prob. 4CP Ch. 14.2 - Prob. 5CP Ch. 14.2 - Prob. 6CP Ch. 14.2 - Prob. 7CP Ch. 14.2 - Prob. 8CP Ch. 14.2 - Prob. 9CP Ch. 14.2 - Prob. 1E Ch. 14.2 - For each of the given functions, find the...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 - Prob. 15E 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 - Prob. 26E Ch. 14.2 - Prob. 27E Ch. 14.2 - Prob. 28E Ch. 14.2 - Prob. 29E Ch. 14.2 - Prob. 30E Ch. 14.2 - Prob. 31E Ch. 14.2 - Prob. 32E Ch. 14.2 - Prob. 33E Ch. 14.2 - Prob. 34E Ch. 14.2 - Prob. 35E Ch. 14.2 - Prob. 36E Ch. 14.2 - Prob. 37E Ch. 14.2 - Find fx,fy,fz, and fyz for the given functions. In...Ch. 14.2 - Prob. 39E Ch. 14.2 - Suppose z=f(x,y) describes the cost to build a...Ch. 14.2 - Prob. 41E Ch. 14.2 - 42. Business The revenue from the sale of x units...Ch. 14.2 - Prob. 62E Ch. 14.2 - Prob. 44E Ch. 14.2 - Prob. 45E Ch. 14.2 - Prob. 43E Ch. 14.2 - Prob. 42E Ch. 14.2 - Prob. 59E Ch. 14.2 - Prob. 50E Ch. 14.2 - Prob. 51E Ch. 14.2 - Work the following applied problems. (See Example...Ch. 14.2 - Prob. 53E Ch. 14.2 - Work the following marginal productivity problems....Ch. 14.2 - Prob. 55E Ch. 14.2 - Prob. 56E Ch. 14.2 - Prob. 58E Ch. 14.2 - Work the following applied problems. (See Example...Ch. 14.2 - Prob. 48E Ch. 14.2 - Prob. 49E Ch. 14.2 - Prob. 61E Ch. 14.2 - Prob. 57E Ch. 14.2 - Prob. 60E Ch. 14.3 - Prob. 1CP Ch. 14.3 - Prob. 2CP Ch. 14.3 - Prob. 3CP Ch. 14.3 - Prob. 4CP Ch. 14.3 - Prob. 1E Ch. 14.3 - Prob. 2E Ch. 14.3 - Prob. 3E Ch. 14.3 - Prob. 4E Ch. 14.3 - Prob. 5E Ch. 14.3 - Prob. 6E Ch. 14.3 - Prob. 7E Ch. 14.3 - 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. 14E Ch. 14.3 - Prob. 13E Ch. 14.3 - Prob. 15E Ch. 14.3 - Prob. 16E Ch. 14.3 - Prob. 17E Ch. 14.3 - Prob. 18E Ch. 14.3 - Prob. 19E Ch. 14.3 - Prob. 20E Ch. 14.3 - Prob. 21E Ch. 14.3 - Prob. 22E 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 - Prob. 29E Ch. 14.3 - Prob. 30E Ch. 14.3 - Prob. 31E Ch. 14.3 - Prob. 32E Ch. 14.3 - Prob. 33E Ch. 14.3 - Prob. 34E Ch. 14.3 - Prob. 35E Ch. 14.3 - Prob. 36E Ch. 14.3 - Prob. 37E Ch. 14.3 - Prob. 38E Ch. 14.3 - Prob. 39E Ch. 14.3 - Prob. 40E Ch. 14.3 - Prob. 41E Ch. 14.3 - Prob. 42E Ch. 14.3 - Prob. 43E Ch. 14.3 - Prob. 44E Ch. 14.4 - Prob. 1CP Ch. 14.4 - Prob. 2CP Ch. 14.4 - Prob. 1E Ch. 14.4 - Prob. 2E Ch. 14.4 - Prob. 3E Ch. 14.4 - Prob. 4E Ch. 14.4 - Prob. 5E Ch. 14.4 - Prob. 6E Ch. 14.4 - Prob. 7E Ch. 14.4 - Prob. 8E Ch. 14.4 - Prob. 9E Ch. 14.4 - Prob. 10E Ch. 14.4 - Prob. 11E Ch. 14.4 - Prob. 12E Ch. 14.4 - Prob. 13E Ch. 14.4 - Prob. 14E Ch. 14.4 - Prob. 15E Ch. 14.4 - Prob. 16E Ch. 14.4 - Prob. 17E Ch. 14.4 - 18. Explain the difference between the two methods...Ch. 14.4 - Prob. 19E Ch. 14.4 - Prob. 20E Ch. 14.4 - Prob. 21E Ch. 14.4 - Prob. 22E Ch. 14.4 - Prob. 23E Ch. 14.4 - Prob. 24E Ch. 14.4 - Prob. 25E Ch. 14.4 - Prob. 26E Ch. 14.4 - Prob. 27E Ch. 14.4 - Prob. 28E Ch. 14.4 - Prob. 29E Ch. 14.4 - Prob. 30E Ch. 14.4 - Prob. 31E Ch. 14.4 - Prob. 32E Ch. 14.4 - Prob. 33E Ch. 14.4 - Prob. 34E Ch. 14.4 - Prob. 35E Ch. 14.4 - Prob. 36E Ch. 14 - Prob. 1RE Ch. 14 - Prob. 2RE Ch. 14 - Prob. 3RE Ch. 14 - Prob. 4RE Ch. 14 - Prob. 5RE 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 - Prob. 32RE 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 - 51. Find positive numbers x and y whose sum is 80...Ch. 14 - Prob. 52RE Ch. 14 - Prob. 53RE Ch. 14 - Prob. 54RE Ch. 14 - Prob. 1CE Ch. 14 - Prob. 2CE

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The second order derivatives ( f x x , f x y ) of the function f ( x , y ) = 4 x 3 y 2 − 4 x y .

Solution Summary: The author explains the second order derivatives of the function f(x,y)=4x3y

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To Calculate: The second order derivatives (fxx,fxy) of the function f(x,y)=4x3y2−4xy.

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Chapter 14 Solutions