. Let f be a function of two variables such that and f(2, 1) = 4. af Ət If, in addition, x = r cost and y = r sint, find the value of when (r, t) = (2,5). 1. f(x, y) = (3x² - 3y, −3x + 3y²) 2. 3. Use the linearization of f at (2, 1) to estimate the value of f(2.02, 0.99). Find the critical points of f, and determine if f has a relative maximum, a relative minimum, or a saddle point at each critical point.

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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I. Let f be a function of two variables such that
and f(2, 1) = 4.
af
Ət
If, in addition, x = r cost and y = r sint, find the value of when
(r, t) = (2, 3).
Use the linearization of f at (2, 1) to estimate the value of f(2.02, 0.99).
Find the critical points of f, and determine if f has a relative
maximum, a relative minimum, or a saddle point at each critical point.
1.
f(x, y) = (3x² − 3y, −3x + 3y²)
2.
3.
Transcribed Image Text:I. Let f be a function of two variables such that and f(2, 1) = 4. af Ət If, in addition, x = r cost and y = r sint, find the value of when (r, t) = (2, 3). Use the linearization of f at (2, 1) to estimate the value of f(2.02, 0.99). Find the critical points of f, and determine if f has a relative maximum, a relative minimum, or a saddle point at each critical point. 1. f(x, y) = (3x² − 3y, −3x + 3y²) 2. 3.
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