ction f(x, y) = [x² + y² if x # (0,0) if x = (0,0) over the x-axis, the y-axis and the two bisector lines. rves (if they exist) corresponding to f(x, y) = k, function is continue but not differentiable in the ne maxima and minima (global and local), if they rectional derivative in every point (x, y) = (0,0), its the points and directions where it takes these
ction f(x, y) = [x² + y² if x # (0,0) if x = (0,0) over the x-axis, the y-axis and the two bisector lines. rves (if they exist) corresponding to f(x, y) = k, function is continue but not differentiable in the ne maxima and minima (global and local), if they rectional derivative in every point (x, y) = (0,0), its the points and directions where it takes these
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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Question
Transcribed Image Text:1.
Consider the function f(x, y) =
√x² + y² if x # (0,0)
if x = (0,0)
0
Evaluate f(x, y) over the x-axis, the y-axis and the two bisector lines.
Find the level curves (if they exist) corresponding to f(x,y) = k,
for k = {-1,1,2}
Verify that this function is continue but not differentiable in the
origin. Find all the maxima and minima (global and local), if they
exist.
Compute the directional derivative in every point (x, y) = (0,0), its
extreme values, the points and directions where it takes these
extreme values.
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