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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)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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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
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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