contestada

Find the absolute maximum and minimum values of f on the set D. f(x, y) = x3 − 3x − y3 + 12y + 4, D is quadrilateral whose vertices are (−2, 3), (2, 3), (2, 2), and (−2, −2).

Respuesta :

Answer:

The maximum of the function is at  [tex]x=1 , y=2[/tex]

Step-by-step explanation:

Remember at that the maximum and minimum of a multivarable function

                                                [tex]\nabla f = 0[/tex]

For this case  

[tex]\nabla f = ( 3x^2 -3 , -3y^2 + 12 ) = ( 0,0)[/tex]

Therefore you have to solve the equations

         [tex]3x^2 -3 = 0\\-3y^2 +12 = 0[/tex]

Solving the equations you get   [tex]x = 1 , y = 2[/tex] , and those points are located at the quadrilateral given.

There are no more critical points.

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