Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and h(x, y) = 2x² + y². a) Find all the local maximum and minimum and saddle points, with their values, for the functions f and h. b) Find all maximum and minimum points and their values for the function h subject to the constraint x² + y² = 3. C) Evaluate the double integral f(x, y) + 3yh(x, y) - 2(x² + y²)]dA, where D is the region bounded by the lines y = 2x, x = 3, and y = 0.
Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and h(x, y) = 2x² + y². a) Find all the local maximum and minimum and saddle points, with their values, for the functions f and h. b) Find all maximum and minimum points and their values for the function h subject to the constraint x² + y² = 3. C) Evaluate the double integral f(x, y) + 3yh(x, y) - 2(x² + y²)]dA, where D is the region bounded by the lines y = 2x, x = 3, and y = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 15E
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![Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and
h(x, y) = 2x² + y².
a)
Find all the local maximum and minimum and saddle points, with
their values, for the functions f and h.
b)
Find all maximum and minimum points and their values for the
function h subject to the constraint x² + y² = 3.
c)
Evaluate the double integral
f(x, y) + 3yh(x, y) - 2(x² + y²)]dA, where D is the region bounded by
the lines y = 2x, x = 3, and y = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27c94875-ab06-496d-8370-359f80afea06%2Fafefa1ae-4faf-494b-9fe9-506b246e09ee%2Fu1xsvml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and
h(x, y) = 2x² + y².
a)
Find all the local maximum and minimum and saddle points, with
their values, for the functions f and h.
b)
Find all maximum and minimum points and their values for the
function h subject to the constraint x² + y² = 3.
c)
Evaluate the double integral
f(x, y) + 3yh(x, y) - 2(x² + y²)]dA, where D is the region bounded by
the lines y = 2x, x = 3, and y = 0.
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