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1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the x-axis, the y-axis and the two bisector line. Find the level curves (if they exist) corresponding to f(x, y) = k, for ke -1,1,2}

1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the x-axis, the y-axis and the two bisector line. Find the level curves (if they exist) corresponding to f(x, y) = k, for ke -1,1,2}

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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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.
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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