1. Consider the function f(x, y) = xy-2x-2y-x² - y². Find Vf and sketch the nullclines (where fx or fy are equal to zero). Find the intersection(s) the nullclines and sketch one vector in each region of the plane. Use that information to determine whether the critical point(s) (intersection(s)) is (are) a maximum, minimum or saddle point. Confirm your result with technology (graph of the vector field, and a 3D graph of the original function). 2. Using the same function as in #1, use the second partials test to verify the results above. 3. Find the absolute extrema of the function f(x, y) = x+y=xy over the region bounded by the triangle with vertices (2,0), (0,2), (0,-2).
1. Consider the function f(x, y) = xy-2x-2y-x² - y². Find Vf and sketch the nullclines (where fx or fy are equal to zero). Find the intersection(s) the nullclines and sketch one vector in each region of the plane. Use that information to determine whether the critical point(s) (intersection(s)) is (are) a maximum, minimum or saddle point. Confirm your result with technology (graph of the vector field, and a 3D graph of the original function). 2. Using the same function as in #1, use the second partials test to verify the results above. 3. Find the absolute extrema of the function f(x, y) = x+y=xy over the region bounded by the triangle with vertices (2,0), (0,2), (0,-2).
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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