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Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x₁+x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite.

Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x₁+x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite.

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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Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x₁ + x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite. Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x² - 4x₁ - 8x₂ b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x²/ d. f(x) = 2x²-3x² - 6x₁x2(x₂-x₁ - 1) e. f(x) = (x₂-x²)² - x²
Transcribed Image Text:Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x₁ + x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite. Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x² - 4x₁ - 8x₂ b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x²/ d. f(x) = 2x²-3x² - 6x₁x2(x₂-x₁ - 1) e. f(x) = (x₂-x²)² - x²
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