Critical points, several variables

[simba_]

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 don't know what the corresponding y values are

df dy = 3y² + 12y + 9 and so y = -3, -1
and here i don't know what the corresponding x values are

 

[Mark44]

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 don't know what the corresponding y values are

df dy = 3y² + 12y + 9 and so y = -3, -1
and here i don't know what the corresponding x values are

f_x = 0 when x = -3 or x = 1
f_y = 0 when y = -3 or y = 1

So both partials are zero at (-3, -3), (-3, 1), (1, -3), and (1, 1).

 

[simba_]

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