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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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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