Q5 - Let ƒ : R³ → R be a C² class function such that ▼ƒ(x*) = (a, 0, –a) and β γ 0 ▼²ƒ(x*) = √√ 8 0 00 8:9) Analyze the following statements, justifying the correct ones and correcting the incorrect ones: a. If ß > 0, ߧ — y² < 0 and (ß8 – y²)¢ < 0 then ï* is a saddle point of f. b. If a = 0, ß < 0, ßồ — 7² > 0 and (ß8 – y²)¢ < 0 then æ* is a local minimum of f. c. If a = 0, ß > 0, ß8 – y² > 0 and (B8 – y²)¢ ≥ 0 then æ* is a global maximum of f.
Q5 - Let ƒ : R³ → R be a C² class function such that ▼ƒ(x*) = (a, 0, –a) and β γ 0 ▼²ƒ(x*) = √√ 8 0 00 8:9) Analyze the following statements, justifying the correct ones and correcting the incorrect ones: a. If ß > 0, ߧ — y² < 0 and (ß8 – y²)¢ < 0 then ï* is a saddle point of f. b. If a = 0, ß < 0, ßồ — 7² > 0 and (ß8 – y²)¢ < 0 then æ* is a local minimum of f. c. If a = 0, ß > 0, ß8 – y² > 0 and (B8 – y²)¢ ≥ 0 then æ* is a global maximum of f.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q5 - Let ƒ : R³ → R be a C² class function such that ▼ƒ(x*) = (a, 0, –a) and
B
Ύ Ο
γ δ ο
00 0 $
▼²ƒ(x*) =
Analyze the following statements, justifying the correct ones and correcting the
incorrect ones:
a. If ß > 0, ߧ – y² < 0 and (ß8 – y²)¢ < 0 then x* is a saddle point of f.
b. If α = 0, ß < 0, ߧ – 7² > 0 and (ß8 − √²)¢ < 0 then ï* is a local minimum of
f.
a
c. If α = 0, ß > 0, ßS — y² > 0 and (B8 – √²)¢ ≥ 0 then æ* is a global maximum
of f.
f(x) = − 1 − 5x + x³ and g(x) = −1− x
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