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. 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 = 2 x 2 − 3 y 2 + 12 y ... ( 1 ) Differentiate equation ( 1 ) with respect to x , z x = 4 x

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.CR, Problem 45CR

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The point where the function have relative extrema and saddle point for the function z=2x2−3y2+12y.

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Chapter 9.CR, Problem 44CR

Chapter 9.CR, Problem 46CR

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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The point where the function have relative extrema and saddle point for the function z = 2 x 2 − 3 y 2 + 12 y .

Solution Summary: The author explains how the discriminant D determines whether the given point is relative extrema or saddle point.

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To find:

The point where the function have relative extrema and saddle point for the function z=2x2−3y2+12y.

Want to see the full answer?

Chapter 9 Solutions

The point where the function have relative extrema and saddle point for the function z = 2 x 2 − 3 y 2 + 12 y .

Solution Summary: The author explains how the discriminant D determines whether the given point is relative extrema or saddle point.

Videos

To find: The point where the function have relative extrema and saddle point for the function z=2x2−3y2+12y.

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=2x2−3y2+12y.