Consider the function f(x, y) = x²y – x² + y² – 6y – 1 and the points A(-1,2) and B(2, –2). %3D 1. Find all critical points of f. At each critical point, determine whether f has a relative minimum, relative maximum or saddle point. 2. Determine the rate of change of f at point A as one moves away from A in the direction towards B.

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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Consider the function f(x, y) = x²y – x² + y² – 6y – 1 and the points A(-1,2) and B(2, –2).
1. Find all critical points of f. At each critical point, determine whether f has a relative
minimum, relative maximum or saddle point.
2. Determine the rate of change of f at point A as one moves away from A in the direction
towards B.
Transcribed Image Text:Consider the function f(x, y) = x²y – x² + y² – 6y – 1 and the points A(-1,2) and B(2, –2). 1. Find all critical points of f. At each critical point, determine whether f has a relative minimum, relative maximum or saddle point. 2. Determine the rate of change of f at point A as one moves away from A in the direction towards B.
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