(a) Let $ g : X \subset \mathbb{R}^n \rightarrow \mathbb{R} $ be a function defined on the finite set $ X $. Does $ g $ achieve a maximum and/or a minimum on $ X $? Explain.(b) Consider the set:\[X = \{ x \in \mathbb{R}^2 : -1 \leq x_1 \leq 1, -1 \leq x_2 \leq 1, x_1 \neq x_2 \},\]and the function $ h : X \rightarrow \mathbb{R} $ defined by:\[h(x) = x_1^2 - 4x_2.\]Are the criteria for the Weierstrass theorem met? Why/why not? Draw some level curves of $ g $. Find the points where the function $ g $ reaches global maximum/a and global minimum/a values, if they exist.

Answered: Image /qna-images/answer/cba6269b-3f15-4985-940c-90ee6f2d7b2f.jpg

b) Consider the set: X = {x € R? : -1 <¤1 < 1, -1 < #2 < 1, x1 # 12} , (2) and the function h : X→R defined by: h(x) = xỉ – 4x2. (3) %3D Are the criteria for the Weierstrass theorem met? Why/why not? Draw some level curves of g. Find the points where the function g reaches global maximum/a and global minimum/a values, if they exist.

b) Consider the set: X = {x € R? : -1 <¤1 < 1, -1 < #2 < 1, x1 # 12} , (2) and the function h : X→R defined by: h(x) = xỉ – 4x2. (3) %3D Are the criteria for the Weierstrass theorem met? Why/why not? Draw some level curves of g. Find the points where the function g reaches global maximum/a and global minimum/a values, if they exist.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

(a) Let $ g : X \subset \mathbb{R}^n \rightarrow \mathbb{R} $ be a function defined on the finite set $ X $. Does $ g $ achieve a maximum and/or a minimum on $ X $? Explain.

(b) Consider the set:

\[
X = \{ x \in \mathbb{R}^2 : -1 \leq x_1 \leq 1, -1 \leq x_2 \leq 1, x_1 \neq x_2 \},
\]

and the function $ h : X \rightarrow \mathbb{R} $ defined by:

\[
h(x) = x_1^2 - 4x_2.
\]

Are the criteria for the Weierstrass theorem met? Why/why not? Draw some level curves of $ g $. Find the points where the function $ g $ reaches global maximum/a and global minimum/a values, if they exist.

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