1. Find all critical points of f. 2. Classify each critical point that you found in part (a) as a local maximum, local minimum, or saddle point. 3. Find the absolute maximum and minimum of f on the region bounded by the x- and y-axes along with the curve xy = 18

1. Find all critical points of f. 2. Classify each critical point that you found in part (a) as a local maximum, local minimum, or saddle point. 3. Find the absolute maximum and minimum of f on the region bounded by the x- and y-axes along with the curve xy = 18

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 18E

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Question

1. Find all critical points of f.

2. Classify each critical point that you found in part (a) as a local maximum, local minimum, or saddle point.

3. Find the absolute maximum and minimum of f on the region bounded by the x- and y-axes along with the curve xy = 18

Consider the function f(x, y) = 2x²y — 6xy – xy² + 3.

Formula Formula A function f(x) attains a local maximum 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 case, f(a) attains a local maximum value f(x) at x=a .

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