Critical points, several variables

  • Thread starter simba_
  • Start date
  • #1
19
0

Homework Statement


Find the critical points of

x3 + y3 + 3x2 + 6y2 - 9x + 9y +1

you do not need to define the critical points

Homework Equations





The Attempt at a Solution



i have
df/dx = 3x2 + 6x - 9 and when i solve this x = -3, 1
but i dont know what the corresponding y values are

df dy = 3y2 + 12y + 9 and so y = -3, -1
and here i dont know what the corresponding x values are
 

Answers and Replies

  • #2
34,884
6,621

Homework Statement


Find the critical points of

x3 + y3 + 3x2 + 6y2 - 9x + 9y +1

you do not need to define the critical points

Homework Equations





The Attempt at a Solution



i have
df/dx = 3x2 + 6x - 9 and when i solve this x = -3, 1
but i dont know what the corresponding y values are

df dy = 3y2 + 12y + 9 and so y = -3, -1
and here i dont know what the corresponding x values are
fx = 0 when x = -3 or x = 1
fy = 0 when y = -3 or y = 1

So both partials are zero at (-3, -3), (-3, 1), (1, -3), and (1, 1).
 
  • #3
19
0
tyty
 

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