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Problem 4. Find all critical points of the function f(x, y) = 2(x² + y²)e−(x²+y²). Note this function has infinitely many critical points. After doing some computation, you should be able to the set of all critical points in the xy-plane with an equation or with a short description in words. You'll also find that the Second Derivative Test is inconclusive. Use the contour plot below, along with CalcPlot3D, to explain whether your critical points are local minima or local maxima.

Problem 4. Find all critical points of the function f(x, y) = 2(x² + y²)e−(x²+y²). Note this function has infinitely many critical points. After doing some computation, you should be able to the set of all critical points in the xy-plane with an equation or with a short description in words. You'll also find that the Second Derivative Test is inconclusive. Use the contour plot below, along with CalcPlot3D, to explain whether your critical points are local minima or local maxima.

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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Problem 4. Find all critical points of the function f(x, y) = 2(x² + y²)e−(x²+y²). Note this function has infinitely many critical points. After doing some computation, you should be able to the set of all critical points in the xy-plane with an equation or with a short description in words. You'll also find that the Second Derivative Test is inconclusive. Use the contour plot below, along with CalcPlot3D, to explain whether your critical points are local minima or local maxima. -2 0.05 01 04658 -1 0.228:4:35 0.7 y -1- 0.6 0.450425 1 0.555 0:20.15 0.35 0.05 X
Transcribed Image Text:Problem 4. Find all critical points of the function f(x, y) = 2(x² + y²)e−(x²+y²). Note this function has infinitely many critical points. After doing some computation, you should be able to the set of all critical points in the xy-plane with an equation or with a short description in words. You'll also find that the Second Derivative Test is inconclusive. Use the contour plot below, along with CalcPlot3D, to explain whether your critical points are local minima or local maxima. -2 0.05 01 04658 -1 0.228:4:35 0.7 y -1- 0.6 0.450425 1 0.555 0:20.15 0.35 0.05 X
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