(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

I have been given a set of functions for which I need to find the stationary points , and determine whether the points are saddle, or max/min.

I think I may have solved it correctly but I end up with all the points being saddle, surely this can't be right.. I may have gone wrong with my arithmetic. Can anyone go through my working. Appreciate the replies.

2. Relevant equations

3. The attempt at a solution

[itex] f(x,y) = x^4 +(2x^2)y -4x^2 +3y^2 [/itex]

[itex]F_{x}[/itex]= [itex]4x^3 +4xy-8x [/itex]

[itex]F_{y}[/itex]=[itex]2x^2+6y [/itex]

[itex]F_{xx}[/itex]12x^2 +4y -8

[itex]F_{yy}[/itex]6

[itex]F_{yx}[/itex]4x

The definition which I have used for delta/ determinant is : If Δ > 0 then stationary points are saddle i.e [itex]f_{xy}^2[/itex] - [itex]f_{xx}[/itex] * [itex]f_{yy}[/itex]

The points which I get are the following:

Re arranging (eq.1) and using eq. 2 (2x^2 = -6y)

4x^3 +4xy-8x (eq.1)

=>

x(4x^2 +4y-8) = 0

x[ (2x^2 +2x^2 ]+4y-8 = 0

x[ (-6y-6y) +4y -8] =0

x(-12+4y-8) = 0

x = 0 , -8y = 8 , y=-1

Points are:

(0,0) , (+/√3, -1)

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Nature of multivariate points

**Physics Forums | Science Articles, Homework Help, Discussion**