Question 2! Let f(x, y) = 1- y³ - 2yx² + 3x² + 3y² and h(x, y) = x² + 2y². 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 = 5. c). Evaluate the double integral [2f(x, y) + yh(x, y) — 6(x² + y²)]dA, where D is the region bounded by the lines y = 3x, y = 2, and x = 0.
Question 2! Let f(x, y) = 1- y³ - 2yx² + 3x² + 3y² and h(x, y) = x² + 2y². 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 = 5. c). Evaluate the double integral [2f(x, y) + yh(x, y) — 6(x² + y²)]dA, where D is the region bounded by the lines y = 3x, y = 2, and x = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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![Question 2
Let
f(x, y) = 1- y³ - 2yx² + 3x² + 3y² and
h(x, y) = x² + 2v².
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 = 5.
c).
Evaluate the double integral
[2f(x, y) + yh(x, y) - 6(x² + y²)]dA,
where D is the region bounded by the lines
y = 3x, y = 2, and x = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c37d3a1-6aac-45fa-85eb-18edb8b8947c%2Fb260e150-dc0e-4365-be44-7ba31924f9b7%2Fp8v416_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
Let
f(x, y) = 1- y³ - 2yx² + 3x² + 3y² and
h(x, y) = x² + 2v².
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 = 5.
c).
Evaluate the double integral
[2f(x, y) + yh(x, y) - 6(x² + y²)]dA,
where D is the region bounded by the lines
y = 3x, y = 2, and x = 0.
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