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ocal extremes of f(x,y) = x³ + y² + 3x² - 3y² - 8. A. Calculate second order partial derivatives of f(x, y). B. Find an equation of a plane tangent to f(x, y). And, use this plane to approx f(1.1,-0.9). C. The critical points of f(x, y) are (0, 0), (-2, 0), (-2, 2). Determine local minimu local maximum points, and saddle points on the surface z = f(x,y).

ocal extremes of f(x,y) = x³ + y² + 3x² - 3y² - 8. A. Calculate second order partial derivatives of f(x, y). B. Find an equation of a plane tangent to f(x, y). And, use this plane to approx f(1.1,-0.9). C. The critical points of f(x, y) are (0, 0), (-2, 0), (-2, 2). Determine local minimu local maximum points, and saddle points on the surface z = f(x,y).

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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8. Local extremes of f(x, y) = x³ + y² + 3x² - 3y² - 8. A. Calculate second order partial derivatives of f(x, y). B. Find an equation of a plane tangent to f(x, y). And, use this plane to approximate f(1.1, -0.9). C. The critical points of f(x, y) are (0, 0), (-2, 0), (-2, 2). Determine local minimum points, local maximum points, and saddle points on the surface z = f(x,y).
Transcribed Image Text:8. Local extremes of f(x, y) = x³ + y² + 3x² - 3y² - 8. A. Calculate second order partial derivatives of f(x, y). B. Find an equation of a plane tangent to f(x, y). And, use this plane to approximate f(1.1, -0.9). C. The critical points of f(x, y) are (0, 0), (-2, 0), (-2, 2). Determine local minimum points, local maximum points, and saddle points on the surface z = f(x,y).
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