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Let f(x, y)=x²-y²=(x-y)(x+y). Use the factored form to sketch the contour f(x, y) = 0 and to find the regions in the xy- plane where f(x, y) >o and the regions where f(x, y) <0. Explain how this sketch shows that the graph of f(x, y) is saddle- shaped at the origin.

Let f(x, y)=x²-y²=(x-y)(x+y). Use the factored form to sketch the contour f(x, y) = 0 and to find the regions in the xy- plane where f(x, y) >o and the regions where f(x, y) <0. Explain how this sketch shows that the graph of f(x, y) is saddle- shaped at the origin.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- Let f(x, y)=x2-y²= (x-y)(x+y). Use the factored form to sketch the contour f(x, y) = 0 and to find the regions in the xy- plane where f(x, y) > o and the regions where f(x, y) <0. Explain how this sketch shows that the graph of f(x, y) is saddle- shaped at the origin.
Transcribed Image Text:- Let f(x, y)=x2-y²= (x-y)(x+y). Use the factored form to sketch the contour f(x, y) = 0 and to find the regions in the xy- plane where f(x, y) > o and the regions where f(x, y) <0. Explain how this sketch shows that the graph of f(x, y) is saddle- shaped at the origin.
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