14. Show that the function f: R²R given by if (x, y) 0, ²+y² f(x, y) 0 if (x, y) = (0,0), is continuously differentiable and has all its second order partial derivatives, but 8² f - (0,0) əxəy 8² f əyəx -(0,0)
14. Show that the function f: R²R given by if (x, y) 0, ²+y² f(x, y) 0 if (x, y) = (0,0), is continuously differentiable and has all its second order partial derivatives, but 8² f - (0,0) əxəy 8² f əyəx -(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:14. Show that the function f: R² → R given by
if (x, y) = 0,
²+y²
f(x, y)
{
0 if (x, y) = (0,0),
is continuously differentiable and has all its second order partial derivatives, but
a² f
8² f
əxəy
-(0,0) = -(0,0)
əyəx
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