Explanation Let function f have continuous second partial derivatives on an open region containing a point ( a , b ) for which f x ( a , b ) = 0 and f y ( a , b ) = 0 . Then the second derivative test discriminant is defined as: d = f x x ( a , b ) f y y ( a , b ) − [ f x y ( a , b ) ] 2 When d > 0 and f x x ( a , b ) > 0 , the Function f has a relative minimumat ( a , b ). When d> 0 and f x x ( a , b ) < 0 , the Function f has a relative maximumat ( a , b ). If d < 0, then ( a , b , f ( a , b )) is a saddle point. The test is inconclusive if d = 0

Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th

11th Edition

ISBN: 9781337275392

Author: Larson, Ron; Edwards, Bruce H.

Publisher: Cengage Learning

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Chapter 13.8, Problem 33E

To determine

For the function f(x,y) at the critical point (x0,y0)

for fxx(x0,y0)=−9,fyy(x0,y0)=6,fxy(x0,y0)=10.;;if there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function.

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Chapter 13.8, Problem 32E

Chapter 13.8, Problem 34E

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Chapter 13 Solutions

Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th

Ch. 13.1 - Think About It Explain why z2=x+3y is not a...Ch. 13.1 - Function of Two Variables What is a graph of a...Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Prob. 6E Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Prob. 9E Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...

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For the function f ( x , y ) at the critical point ( x 0 , y 0 ) for f x x ( x 0 , y 0 ) = − 9 , f y y ( x 0 , y 0 ) = 6 , f x y ( x 0 , y 0 ) = 10 .;;if there is a relative maximum , a relative minimum, a saddle point, or insufficient information to determine the nature of the function.

For the function f(x,y) at the critical point (x0,y0) for fxx(x0,y0)=−9,fyy(x0,y0)=6,fxy(x0,y0)=10.;;if there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function.

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Chapter 13 Solutions

For the function f(x,y) at the critical point (x0,y0)

for fxx(x0,y0)=−9,fyy(x0,y0)=6,fxy(x0,y0)=10.;;if there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function.