Explanation Given: A function f ( x , y ) has the partial derivative f x ( 1 , 2 ) = 3 and f y ( 1 , 2 ) = 5 . Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Mathematically, f x ( x 0 , y 0 ) = 0 f y ( x 0 , y 0 ) = 0 Let us assume that ( x 0 , y 0 ) is the critical point of a continuous function f and D be calculated as follows: D = f x x ( x 0 , y 0 ) f y y ( x 0 , y 0 ) − f x y ( x 0 , y 0 ) 2 Then, If D > 0 and f x x ( x 0 , y 0 ) > 0 , then the function has local minimum at ( x 0 , y 0 ) If D > 0 and f x x <

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 8.5, Problem 26P

To determine

A function f(x,y) has the partial derivative fx(1,2)=3 and fy(1,2)=5. Explain how you know that f does not have minimum at (1,2).

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Chapter 8.5, Problem 25P

Chapter 8.5, Problem 27P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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Knowledge Booster

A function f ( x , y ) has the partial derivative f x ( 1 , 2 ) = 3 and f y ( 1 , 2 ) = 5 . Explain how you know that f does not have minimum at ( 1 , 2 ) .

A function f(x,y) has the partial derivative fx(1,2)=3 and fy(1,2)=5. Explain how you know that f does not have minimum at (1,2).

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Chapter 8 Solutions