Explanation Given information: The given function is f ( x , y ) = 3 x e y − x 3 − e 3 y . Calculation: Consider the function, f ( x , y ) = 3 x e y − x 3 − e 3 y …… (1) Differentiate equation (1) with respect to x . f x = d d x ( 3 x e y − x 3 − e 3 y ) 0 = 3 e y − 3 x 2 x 2 = e y Differentiate equation (1) with respect to y . f y = d d y ( 3 x e y − x 3 − e 3 y ) 0 = 3 x e y − 3 e 3 y e y ( x − 1 ) = 0 So, x = 1 Now, x 2 = e y 1 2 = e y 1 = e y y = 0 So, the critical point is ( 1 , 0 ) Now, f x x is calculated as, f x x = d d x ( 3 e y − 3 x 2 ) = − 6 x Now, f y y is calculated as, f y y = ∂ ∂ y ( 3 x e y − 3 e 3 y ) = 3 x e y − 9 e 3 y Now, f y x

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 11.7, Problem 54PS

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To show: The function has exactly one critical point and it correspond to relative maximum and whether its an absolute maximum.

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Chapter 11.7, Problem 53PS

Chapter 11.7, Problem 55PS

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Chapter 11 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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The function has exactly one critical point and it correspond to relative maximum and whether its an absolute maximum.

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Chapter 11 Solutions