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1: Consider the following function. h(u, v) = u³ + 30uv – 15v2 (a) Find the critical points of h. (b) For each critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point. Separate your answers with a comma. Your first value of D must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of D must correspond with the second critical point. (c) Use the Second Partials 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), (-20, –20) (B) (0, 0), (-10, –10) (C) (0, 0), (10, 10) (D) (0, 0). (20, –20) (E) (0, 0). (10. –10) (F) (0, 0), (-10, 10) (G) (0, 0), (20, 20) (H) (0, 0), (-20, 20)

1: Consider the following function. h(u, v) = u³ + 30uv – 15v2 (a) Find the critical points of h. (b) For each critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point. Separate your answers with a comma. Your first value of D must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of D must correspond with the second critical point. (c) Use the Second Partials 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), (-20, –20) (B) (0, 0), (-10, –10) (C) (0, 0), (10, 10) (D) (0, 0). (20, –20) (E) (0, 0). (10. –10) (F) (0, 0), (-10, 10) (G) (0, 0), (20, 20) (H) (0, 0), (-20, 20)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.3: Partial Fractions
Problem 2E
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Options for (c): 

(A) Relative Maximum, Relative Minimum   (B) Inconclusive, Relative Maximum   (C) Saddle Point, Saddle Point   (D) Inconclusive, Relative Minimum   (E) Relative Miniumum, Relative Maximum   (F) Saddle Point, Relative Minimum   (G) Saddle Point, Relative Maximum   (H) Inconclusive, Saddle Point   
1: Consider the following function. h(u, v) = u³ + 30uv – 15v2 (a) Find the critical points of h. (b) For each critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point. Separate your answers with a comma. Your first value of D must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of D must correspond with the second critical point. (c) Use the Second Partials 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), (-20, –20) (B) (0, 0), (-10, –10) (C) (0, 0), (10, 10) (D) (0, 0). (20, –20) (E) (0, 0). (10, –10) (F) (0, 0), (-10, 10) (G) (0, 0), (20, 20) (H) (0, 0), (-20, 20)
Transcribed Image Text:1: Consider the following function. h(u, v) = u³ + 30uv – 15v2 (a) Find the critical points of h. (b) For each critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point. Separate your answers with a comma. Your first value of D must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of D must correspond with the second critical point. (c) Use the Second Partials 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), (-20, –20) (B) (0, 0), (-10, –10) (C) (0, 0), (10, 10) (D) (0, 0). (20, –20) (E) (0, 0). (10, –10) (F) (0, 0), (-10, 10) (G) (0, 0), (20, 20) (H) (0, 0), (-20, 20)
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