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By first computing the partial derivatives, find any points at which f(x, y) = 2x - x² − (y + 2)² may have a local maximum.

By first computing the partial derivatives, find any points at which f(x, y) = 2x - x² − (y + 2)² may have a local maximum.

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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Let z = f(x, y) be a differentiable function, and suppose that at the point (xo, yo), f achieves a local maximum. That is, the value of f(xo, yo) is greater than the value of f(x, y) for all (x, y) nearby (xo, yo). You might find it helpful to sketch a rough picture of a possible function f that has this property. By first computing the partial derivatives, find any points at which f(x, y) = 2x − x² − (y + 2)² may have a local maximum. -
Transcribed Image Text:Let z = f(x, y) be a differentiable function, and suppose that at the point (xo, yo), f achieves a local maximum. That is, the value of f(xo, yo) is greater than the value of f(x, y) for all (x, y) nearby (xo, yo). You might find it helpful to sketch a rough picture of a possible function f that has this property. By first computing the partial derivatives, find any points at which f(x, y) = 2x − x² − (y + 2)² may have a local maximum. -
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