Problem #3: Consider the following function. f(x, y) = 2x3+24xy-12y2 (a) Find the critical points of f. (b) For each critical point in (a), find the value of det[H(xo, yo)] from the Second Derivative test that is used to classify the critical point. Separate your answers with a comma. Your first value of det[H(xo, yo)] must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of det[H(xo, yo)] must correspond with the second critical point. (c) Use the Second Derivative test to classify each critical point from (a). Note that for each given answer, the first classification corresponds to the first critical point in (a) [i.e., the critical point (0,0)] and the second classification corresponds to the second critical point in (a). (A) (0, 0), (2, 2) (F) (0, 0), (4, 4) (B) (0, 0), (-4,-4) (C) (0, 0), (2,-2) (D) (0, 0), (4,-4) (E) (0, 0), (-2,-2) (G) (0, 0), (-4, 4) (H) (0, 0), (-2, 2)
Problem #3: Consider the following function. f(x, y) = 2x3+24xy-12y2 (a) Find the critical points of f. (b) For each critical point in (a), find the value of det[H(xo, yo)] from the Second Derivative test that is used to classify the critical point. Separate your answers with a comma. Your first value of det[H(xo, yo)] must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of det[H(xo, yo)] must correspond with the second critical point. (c) Use the Second Derivative test to classify each critical point from (a). Note that for each given answer, the first classification corresponds to the first critical point in (a) [i.e., the critical point (0,0)] and the second classification corresponds to the second critical point in (a). (A) (0, 0), (2, 2) (F) (0, 0), (4, 4) (B) (0, 0), (-4,-4) (C) (0, 0), (2,-2) (D) (0, 0), (4,-4) (E) (0, 0), (-2,-2) (G) (0, 0), (-4, 4) (H) (0, 0), (-2, 2)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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![Problem #3: Consider the following function.
f(x, y) = 2x3+24xy-12y2
(a) Find the critical points of f.
(b) For each critical point in (a), find the value of det[H(xo, yo)] from the Second
Derivative test that is used to classify the critical point.
Separate your answers with a comma. Your first value of det[H(xo, yo)] must
correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your
second value of det[H(xo, yo)] must correspond with the second critical point.
(c) Use the Second Derivative test to classify each critical point from (a).
Note that for each given answer, the first classification corresponds to the first critical
point in (a) [i.e., the critical point (0,0)] and the second classification corresponds to
the second critical point in (a).
(A) (0, 0), (2, 2)
(F) (0, 0), (4, 4)
(B) (0, 0), (-4,-4) (C) (0, 0), (2,-2) (D) (0, 0), (4,-4) (E) (0, 0), (-2,-2)
(G) (0, 0), (-4, 4) (H) (0, 0), (-2, 2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8a9802b-ded9-4a7b-93c8-71218002814a%2F6a892fb6-ff99-4062-8a57-d615828ec4c5%2Fk6x71w8_processed.png&w=3840&q=75)
Transcribed Image Text:Problem #3: Consider the following function.
f(x, y) = 2x3+24xy-12y2
(a) Find the critical points of f.
(b) For each critical point in (a), find the value of det[H(xo, yo)] from the Second
Derivative test that is used to classify the critical point.
Separate your answers with a comma. Your first value of det[H(xo, yo)] must
correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your
second value of det[H(xo, yo)] must correspond with the second critical point.
(c) Use the Second Derivative test to classify each critical point from (a).
Note that for each given answer, the first classification corresponds to the first critical
point in (a) [i.e., the critical point (0,0)] and the second classification corresponds to
the second critical point in (a).
(A) (0, 0), (2, 2)
(F) (0, 0), (4, 4)
(B) (0, 0), (-4,-4) (C) (0, 0), (2,-2) (D) (0, 0), (4,-4) (E) (0, 0), (-2,-2)
(G) (0, 0), (-4, 4) (H) (0, 0), (-2, 2)
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