Let f(x.y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is enough to conclude that (1,-2) is a saddle point? 1. fxx (1,-2) < 0 and fyy (1.-2) < 0. II. fxy (1,-2) < 0. II. frx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2). IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2) a. II O b.1 OC. IV d. Il

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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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 f(x.y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is
enough to conclude that (1,-2) is a saddle point?
1. fxx (1,-2) < 0 and fyy (1.-2) < 0.
II. fxy (1,-2) < 0.
II. frx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2).
IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2)
a. II
O b.1
OC. IV
d. Il
Transcribed Image Text:Let f(x.y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is enough to conclude that (1,-2) is a saddle point? 1. fxx (1,-2) < 0 and fyy (1.-2) < 0. II. fxy (1,-2) < 0. II. frx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2). IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2) a. II O b.1 OC. IV d. Il
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