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Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this function.

Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this function.

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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PART B: Let z = f(x, y) = 5x – x³ + 2xy – y². Find and classify all the critical point(s) of this function. • You must show your steps in solving. You must also clearly compute all second partials and D value(s) and fully use the second derivative test, showing calculations and putting a box around your conclusion(s). You do NOT have to find the z value(s) at the critical point(s). • You may or may not have all three types. Just type in and label what you found. Type in something like: " local min at (?,?); local max at (?, ?); saddle point at (?,?)
Transcribed Image Text:PART B: Let z = f(x, y) = 5x – x³ + 2xy – y². Find and classify all the critical point(s) of this function. • You must show your steps in solving. You must also clearly compute all second partials and D value(s) and fully use the second derivative test, showing calculations and putting a box around your conclusion(s). You do NOT have to find the z value(s) at the critical point(s). • You may or may not have all three types. Just type in and label what you found. Type in something like: " local min at (?,?); local max at (?, ?); saddle point at (?,?)
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