A surface is represented by the following multivariable function, f(x,y)=x^3+y^3-3x-3y+1 Calculate coordinates of stationary points.

ruigE 2021-02-18 Answered
A surface is represented by the following multivariable function,
f(x,y)=x3+y33x3y+1
Calculate coordinates of stationary points.
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Expert Answer

Viktor Wiley
Answered 2021-02-19 Author has 84 answers
Obtain fxandfy as follows.
fx(x,y)=x(x3+y33x3y+1)
=3x2+030+0
=3x23
fy(x,y)y(x3+y33x3y+1)
=0+3y203+0
=3y23
Now obtain fx=0andfy=0 as follows.
fx=0
3x23=0
3(x21)=0
x21=0
x2=1
x=1
x=±1
fy=0
3y23=0
3(y21)=0
y21=0
y2=1
y=1
y=±1
Thus, the coordinates of stationary points are P1(1,1),P2(1,1),P3(1,1),andP4(1,1).
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