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f(x, y) = x² - 9xy + y² + 7y + 1 Local maxima are Local minima are Saddle points are II III m

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.6: Quadratic Functions

Problem 36E

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Question

Determine saddle points, all local minima and local maxima. Enter each point as an ordered triple, e.g., "(1,5,10)". If there's more than one point of a given type, write out a comma-separated list of ordered triples. If there are no points of a given type, say there is "none".

f(x, y) = x² - 9xy + y² + 7y + 1
Local maxima are
Local minima are
Saddle points are
II
III
m

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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