Recent content by dispiriton

From negative definite we can conclude f_xx and f_yy are negative but the same cannot be concluded for f_xy. Thus how do we conclude that when the Hessian is negative the expansion becomes f(P) minus something. Is it possible for the terms behind f(P) to add up to a positive number if f_xy is...

But when the Hessian is negative definite we can only say that f_xx and f_yy are negative. Can the same be concluded for the f_xy term?

How do I use Taylor Series to show f(P) is a local maximum at a stationary point P if the Hessian matrix is negative definite. I understand that some of the coefficients of the terms of the taylor series expansion are the coordinates of the Hessian matrix but for the f_xy term there is no...

Its sort of like the "bar" where it is the conjugate.

Homework Statement I am told to try and solve <x - ty, x - ty> where t = <x,y>/<y,y> However, I am stuck at that equation and unable to manipulate it to get rid of the * Homework Equations The Attempt at a Solution <x - ty, x - ty> = <x,x> - <x,ty> - <ty,x> + <ty,ty>...

So after I've found direction of tangent line to the two curves I cross them to find a normal vector to plane which i use to define the plane. But this final plane I define, is it the equation of the tangent plane through P already or is it only the equation of the surface?

Homework Statement I need to find the tangent plane of a surface S at a point P without being given the eqn of the surface. I am also given that two curves lie on this surface Homework Equations Point P: (2,1,3) Curve 1: <2+3t, 1 - (t^2), 3 - 4t + (t^2)> Curve 2: <1+ (u^2), 2(u^3) -...

Homework Statement In general how do i parametrize a circle of radius r at centre (a,b,c) laying on a plane? E.g. (x + y + z = 6) Homework Equations The Attempt at a Solution