Answered: Hello, I need help for the problems…

Hello, I need help for the problems attached below: Q6. What is the local minimum value of f(x_1,x_2)=x_1^2 + 2x_1x_2 + x_2^3? Round your answer to two digits.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 14BEXP

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Question

Hello,

I need help for the problems attached below:

Q6. What is the local minimum value of f(x_1,x_2)=x_1^2 + 2x_1x_2 + x_2^3? Round your answer to two digits.

Q7. What is the global maximum value of f(x1,x2)=lnx1+lnx2 with constraint 2x1+3x2=6? Round your answer to two digits.

Many thanks

George

7. What is the global maximum value of f(x1, x2) = ln ¤1 + ln x2 with constraint 2x1 +3x2 = 6? Round your
answer to two digits.

6. What is the local minimum value of f(x1, x2) = xị + 2x1x2 + xž? Round your answer to two digits.

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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