Can someone please solve the following problem showing all steps and the solutio

Question

Can someone please solve the following problem showing all steps and the solution? Any help will be greatly appreciated but I will award all the points to the most complete and thorough correct answer. Thanks!!!

Can someone please solve the following problem showing all steps and the solution? Any help will be greatly appreciated but I will award all the points to the most complete and thorough correct answer. Thanks!!! Find and classify all critical points for the function f (x,y) = 2x^3 +xy^2 +5x^2 +y^2

Explanation / Answer

FIRST FIND:

fx =0 and fy =0  

solve these equations to get critical points..

say:

fx  =6x2 + y2 +10x = 0

fy=2xy +2y = 0

solving these two equations we get:

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