Problem #3: Consider the following function. f(x, y) = x3+18xy-912 (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), (6,6) (B) (0,0), (6,-6) (C) (0, 0), (-12, -12) (D) (0, 0), (12, 12) (E) (0, 0), (12,-12) (F) (0, 0), (-6,-6) (G) (0, 0), (-6,6) (H) (0,0), (-12, 12)
Problem #3: Consider the following function. f(x, y) = x3+18xy-912 (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), (6,6) (B) (0,0), (6,-6) (C) (0, 0), (-12, -12) (D) (0, 0), (12, 12) (E) (0, 0), (12,-12) (F) (0, 0), (-6,-6) (G) (0, 0), (-6,6) (H) (0,0), (-12, 12)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Problem #3: Consider the following function.
f(x, y) = x3+18xy-912
(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), (6,6) (B) (0,0), (6,-6) (C) (0, 0), (-12, -12) (D) (0, 0), (12, 12) (E) (0, 0), (12,-12)
(F) (0, 0), (-6,-6) (G) (0, 0), (-6,6) (H) (0,0), (-12, 12)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76dba93-23d2-47f1-b92c-ad2c0bf14e16%2Faf9d9ad6-d572-437d-b945-bd87839f8fd5%2Fplp0v8_processed.png&w=3840&q=75)
Transcribed Image Text:Problem #3: Consider the following function.
f(x, y) = x3+18xy-912
(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), (6,6) (B) (0,0), (6,-6) (C) (0, 0), (-12, -12) (D) (0, 0), (12, 12) (E) (0, 0), (12,-12)
(F) (0, 0), (-6,-6) (G) (0, 0), (-6,6) (H) (0,0), (-12, 12)
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