1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3, -3). (b) Use the tangent plane to provide an approximation to the function value at (x, y) = (-3.01, -2.95) and then (x, y) = (-3.1, –-2.9). (c) If you compare the approximations with the exact function value at the respective point (so compare the estimation at (-3.01, -2.95) with the function value at (-3,-3), and similarly for the other point), which approximation is more accurate? Explain why. [10 morlkal
1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3, -3). (b) Use the tangent plane to provide an approximation to the function value at (x, y) = (-3.01, -2.95) and then (x, y) = (-3.1, –-2.9). (c) If you compare the approximations with the exact function value at the respective point (so compare the estimation at (-3.01, -2.95) with the function value at (-3,-3), and similarly for the other point), which approximation is more accurate? Explain why. [10 morlkal
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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Transcribed Image Text:1. Consider the function f (x, y) = -
70 - 4x2 – y2.
(a) Find the tangent plane to f (x, y) at (-3, –3).
(b) Use the tangent plane to provide an approximation to the function value at (x, y) = (-3.01, -2.95) and then
(x, y) = (-3.1, –2.9).
(c) If you compare the approximations with the exact function value at the respective point (so compare the
estimation at (-3.01, -2.95) with the function value at (-3, –3), and similarly for the other point), which
approximation is more accurate? Explain why.
[10 morlkal
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