Explanation Approach: Let f x ( a , b ) = 0 and f y ( a , b ) = 0 . The discriminant D = f x x ( a , b ) ⋅ f y y ( a , b ) − [ f x y ( a , b ) ] 2 decides whether the given point is relative extrema or saddle point, if it satisfies the following conditions. a. f ( a , b ) is a relative maximum if D > 0 and f x x ( a , b ) < 0 . b. f ( a , b ) is a relative minimum if D > 0 and f x x ( a , b ) > 0 . c. f ( a , b ) is a saddle point (neither a maximum nor a minimum) if D < 0 . d. if D = 0 , the test gives no information. Calculation: Consider the function, z = x 3 + y 2 + 2 x y − 4 x − 3 y − 2... ( 1 ) Differentiate equation ( 1 ) with respect to x , z x = 3 x 2 + 2 y − 4... ( 2 ) Differentiate equation ( 2 ) with respect to x , z x x = 6 x Differentiate equation ( 2 ) with respect to y , z x y = 2 Differentiate equation ( 1 ) with respect to y , z y = 2 y + 2 x − 3

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 9.CR, Problem 51CR

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The point where the function have relative extrema and saddle point for the function z=x3+y2+2xy−4x−3y−2.

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Chapter 9.CR, Problem 50CR

Chapter 9.CR, Problem 52CR

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The point where the function have relative extrema and saddle point for the function z = x 3 + y 2 + 2 x y − 4 x − 3 y − 2 .

Solution Summary: The author explains that the discriminant D=f_xx(a,b)cdot determines whether the given point is relative extrema or saddle point, if it

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To find:

The point where the function have relative extrema and saddle point for the function z=x3+y2+2xy−4x−3y−2.

Want to see the full answer?

Chapter 9 Solutions

The point where the function have relative extrema and saddle point for the function z = x 3 + y 2 + 2 x y − 4 x − 3 y − 2 .

Solution Summary: The author explains that the discriminant D=f_xx(a,b)cdot determines whether the given point is relative extrema or saddle point, if it

Videos

To find: The point where the function have relative extrema and saddle point for the function z=x3+y2+2xy−4x−3y−2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The point where the function have relative extrema and saddle point for the function z=x3+y2+2xy−4x−3y−2.