Let f(x, y) = x² + y² – 2a°y- if (x, y) # (0,0), - (14 + y²)² ' and f(0, 0) = 0. Show that f is continuous at the origin; • f has a minimum at (0,0) along any straight line through (0,0); f has NO minimum at (0,0).
Let f(x, y) = x² + y² – 2a°y- if (x, y) # (0,0), - (14 + y²)² ' and f(0, 0) = 0. Show that f is continuous at the origin; • f has a minimum at (0,0) along any straight line through (0,0); f has NO minimum at (0,0).
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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Transcribed Image Text:Let
f(x, y) = x² + y? – 2x°y
4x°y?
(r4 + y?)2 '
if (x, y) # (0,0),
and f(0,0) = 0. Show that
• f is continuous at the origin;
f has a minimum at (0,0) along any straight line through (0,0);
f has NO minimum at (0,0).
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