Answered: Consider the function f(x, y) = 3x^2 +…

Consider the function f(x, y) = 3x^2 + 4xy + 2y^2 - 12x - 16y . Find the critical points of f and determine whether each is a local maximum, local minimum, or saddle point.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

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

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

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 19E

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Question

Consider the function f(x, y) = 3x^2 + 4xy + 2y^2 - 12x - 16y .

Find the critical points of f and determine whether each is a local maximum, local minimum, or saddle point.

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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