Suppose that P is a critical point of z = f (x, y).Suppose further that at P, the following hold:a² fმ2a² fdy²–3,-2,8² fa² fəyəxმე მყWhat can we say about point P?○ Vƒ(P) 0−1.The function has a local minimum at PThe function has a local maximum at PThe function has a saddle point at P

Answered: Suppose that P is a critical point of z…

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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Question

Suppose that P is a critical point of z = f (x, y).
Suppose further that at P, the following hold:
a² f
მ2
a² f
dy²
–3,
-2,
8² f
a² f
əyəx
მე მყ
What can we say about point P?
○ Vƒ(P) 0
−1.
The function has a local minimum at P
The function has a local maximum at P
The function has a saddle point at P

Expert Solution

Step 1: Define the problem

Given that P is a critical point P of $z equals f open parentheses x comma y close parentheses$

$fraction numerator partial differential squared f over denominator partial differential x squared end fraction equals negative 3 comma fraction numerator partial differential squared f over denominator partial differential y squared end fraction equals negative 2 comma fraction numerator partial differential squared f over denominator partial differential y partial differential x end fraction equals fraction numerator partial differential squared f over denominator partial differential x partial differential y end fraction equals negative 1$