# Thread: Calculus 3 Maximizations Problem (Need major help with this question!)

1. ## Calculus 3 Maximizations Problem (Need major help with this question!)

I have:

f(x,y): http://www.wolframalpha.com/input/?i=(x^6+*+y^4+*+(4+-+x+-+y)^7)

∂f/∂x: http://www.wolframalpha.com/input/?i=-x^5+(13+x%2B6+(-4%2By))+y^4+(-4%2Bx%2By)^6+%3D+0,+Solve+for+x

∂f/∂y: http://www.wolframalpha.com/input/?i=-x^6+y^3+(-4%2Bx%2By)^6+(-16%2B4+x%2B11+y)+%3D+0,+Solve+for+x

∂^2 f/(∂x ∂y): http://www.wolframalpha.com/input/?i=-2+x^5+y^3+(-4%2Bx%2By)^5+(192-152+x%2B26+x^2-180+y%2B80+x+y%2B33+y^2)+%3D+0,+Solve+for+x

where I told Wolfram Alpha to isolate x for each equation with partial derivatives because I think that's what I need to do in order to get the critical points.

I'm confused as to what I need to do next. I heard about a Hessian matrix method but I don't know if that's necessary or if I can just do a regular system of equations. I read the Paul's Online Notes website but I'm still stuck for this particular problem.

What do I do when I solve for x when each of the equations are equal to 0? If anything is unclear, just ask me to clarify it.

Any input would be appreciated!

2. ## Re: Calculus 3 Maximizations Problem (Need major help with this question!)

Originally Posted by s3a
I have:

f(x,y): http://www.wolframalpha.com/input/?i=(x^6+*+y^4+*+(4+-+x+-+y)^7)

∂f/∂x: http://www.wolframalpha.com/input/?i=-x^5+(13+x%2B6+(-4%2By))+y^4+(-4%2Bx%2By)^6+%3D+0,+Solve+for+x

∂f/∂y: http://www.wolframalpha.com/input/?i=-x^6+y^3+(-4%2Bx%2By)^6+(-16%2B4+x%2B11+y)+%3D+0,+Solve+for+x

∂^2 f/(∂x ∂y): http://www.wolframalpha.com/input/?i=-2+x^5+y^3+(-4%2Bx%2By)^5+(192-152+x%2B26+x^2-180+y%2B80+x+y%2B33+y^2)+%3D+0,+Solve+for+x

where I told Wolfram Alpha to isolate x for each equation with partial derivatives because I think that's what I need to do in order to get the critical points.

I'm confused as to what I need to do next. I heard about a Hessian matrix method but I don't know if that's necessary or if I can just do a regular system of equations. I read the Paul's Online Notes website but I'm still stuck for this particular problem.

What do I do when I solve for x when each of the equations are equal to 0? If anything is unclear, just ask me to clarify it.

Any input would be appreciated!