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Suppose f(x, y) = x² + y² – 10x − 10y + 2 (A) How many critical points does f have in R²? 1 (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. 4 (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. N (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. N (E) What is the maximum value of f on R2? If there is none, type N. N (F) What is the minimum value of f on R²? If there is none, type N.

Suppose f(x, y) = x² + y² – 10x − 10y + 2 (A) How many critical points does f have in R²? 1 (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. 4 (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. N (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. N (E) What is the maximum value of f on R2? If there is none, type N. N (F) What is the minimum value of f on R²? If there is none, type N.

Advanced Engineering Mathematics
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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Suppose f(x, y) = x² + y² − 10x − 10y + 2 (A) How many critical points does f ƒ have in R²? 1 (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. 4 (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. N (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. N (E) What is the maximum value of f on R²? If there is none, type N. N (F) What is the minimum value of f on R²? If there is none, type N.
Transcribed Image Text:Suppose f(x, y) = x² + y² − 10x − 10y + 2 (A) How many critical points does f ƒ have in R²? 1 (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. 4 (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. N (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. N (E) What is the maximum value of f on R²? If there is none, type N. N (F) What is the minimum value of f on R²? If there is none, type N.
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