For the function:   z=cos^3(x)cos^3(y) a. Find and classify all of its critical points. b. Tell how to use the contour map of the surface to show the critical points and the behavior of the level curves near those points. Use this information to explain the contour map of the selected surface.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the function:   z=cos^3(x)cos^3(y)

a. Find and classify all of its critical points.

b. Tell how to use the contour map of the surface to show the critical points and the behavior of the level curves near those points. Use this information to explain the contour map of the selected surface.

c. Choose any point of interest on the surface.
1.  Find the equation of the tangent plane and the parametric equations of the normal line to the surface at that point.
2.  Sketch a graph, using an app (Wolfram Mathematica, Scilab, Fusion 360 or else), where you show the surface, the tangent plane, and the normal line to the surface at the selected point.

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