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Given the function f(r. y) = 1² + y² + 1 • For every point (r. y) = R², compute the gradient and the Hexian matrix. Sketch the level curves corresponding to the values of f(x,y)=k, for k = {1,.2.3} • Find all the local maxima/minima/saddles of the function. Estabilish (justify) if the global maximum/minimum of the function exist or not and, in case, find them . Find the maximum and/or the minimum of the function (if they exist) over the following sets of points: A = {(r, y) = R²: x² + y² = 1} B = {(x, y) = R²: x² + y² ≤ 1} C = {(x,y) = R²: y=x}

Given the function f(r. y) = 1² + y² + 1 • For every point (r. y) = R², compute the gradient and the Hexian matrix. Sketch the level curves corresponding to the values of f(x,y)=k, for k = {1,.2.3} • Find all the local maxima/minima/saddles of the function. Estabilish (justify) if the global maximum/minimum of the function exist or not and, in case, find them . Find the maximum and/or the minimum of the function (if they exist) over the following sets of points: A = {(r, y) = R²: x² + y² = 1} B = {(x, y) = R²: x² + y² ≤ 1} C = {(x,y) = R²: y=x}

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Given the function f(x,y) = 1² + y² + 1 . • For every point (r. y) = R², compute the gradient and the Hexian matrix. Sketch the level curves corresponding to the values of f(x,y)=k, for k = {1,2,3} • Find all the local maxima/minima/saddles of the function. Estabilish (justify) if the global maximum/minimum of the function exist or not and, in case, find them • Find the maximum and/or the minimum of the function (if they exist) over the following sets of points: A = {(x,y) € R² : x² + y² = 1} B = {(x, y) = R²: x² + y² ≤ 1} € C = {(x, y) = R²: y=r}
Transcribed Image Text:1. Given the function f(x,y) = 1² + y² + 1 . • For every point (r. y) = R², compute the gradient and the Hexian matrix. Sketch the level curves corresponding to the values of f(x,y)=k, for k = {1,2,3} • Find all the local maxima/minima/saddles of the function. Estabilish (justify) if the global maximum/minimum of the function exist or not and, in case, find them • Find the maximum and/or the minimum of the function (if they exist) over the following sets of points: A = {(x,y) € R² : x² + y² = 1} B = {(x, y) = R²: x² + y² ≤ 1} € C = {(x, y) = R²: y=r}
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