The Partial Derivative Test

find the critical values for f(x,y)=6xy^2 -2x^3 - 3y^4 test and classify the nature of the extrema

Question

The Partial Derivative Test

find the critical values for f(x,y)=6xy^2 -2x^3 - 3y^4 test and classify the nature of the extrema

serenity74 · Answer

Calculus is life lol you don't question you just do it XD JK.

zarkon · Answer

what have you tried?

anonymous · Answer

fx=6y^2-6x^2     fy=12xy-12y^3

anonymous · Answer

i set fx equal to 0 and got x=y

zarkon · Answer

can you first spot the "obvious" solution

anonymous · Answer

no

zarkon · Answer

notice x=0 and y=0 is a solution

zarkon · Answer

then 

$$f_y=12xy-12y^3 =0$$

$$y(12x-12y^2)=0$$

so 

$$12x-12y^2=0$$

zarkon · Answer

$$f_x=6y^2-6x^2=0 $$

so

$$12y^2-12x^2=0 $$

zarkon · Answer

add
$$12x-12y^2=0$$

and 
$$12y^2-12x^2=0$$


then solve for x

anonymous · Answer

what do you mean add?

anonymous · Answer

if we know x=0 and y=0 then (0,0)

anonymous · Answer

shouldnt we use the determinant fxx*fyy-(fx)^2 to test its extrema?