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Determine the absolute extrema of this function and plot its surface?

Posted 1 month ago
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How do you solve these problems using mathematica?

Attachment

Through[{Minimize, Maximize}[{2 x^3 + y^4, Norm[{x, y}] <= 1}, {x, y}]]

to visualize

 Plot3D[2 x^3 + y^4, {x, -1.4, 1.4}, {y, -1.4, 1.4}, 
  RegionFunction -> ({x, y} \[Function] x^2 + y^2 < 1), 
  MeshFunctions -> {#3 &}]

For Question 2

 RegionNearest[ImplicitRegion[x^2 + y^2 == z, {x, y, z}], {5, 5, 0}]
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