# Calculus Questions - HELP

1. Dec 17, 2003

### jherasjr

Calculus Questions - HELP!!!!!

1. Consider the cube determined by the planes x=-1, x=3, y=5, y=9,
z=0, and z=4.

a) Give the coordinates of the eight vertices and center of
the cube.

b) Determine an equation of the largest sphere contained in
the cube.

c) Determine an equation of the largest sphere that would fit
between the sphere found in (b) and the cube.

2. Determine an equation of a plane that intersects the plane
x+y+z=3 at an angle of 60 degrees.

3. a) Determine an equation of the tangent plane to the surface
given by x^2*y+y^2*z+z^2*x=1 at the point (1,0,1).

b) Determine an equation of the line that is normal to the
surface given by x^2*y+y^2*z+z^2*x=1 at the point (1,0,1).

4. Prove that u+v+w=0, then u*v=v*w, and u*w=w*v. What is the
geometric interpretation of these relationships?

5. Suppose f(x,y)=A*X^3+B*X*Y+C*Y^2, where A, B, and C are
constants. For what values of A, B, and C does f have a
critical value at (-2,1)? Determine what type of critical
point it is.

6. Determine the maximum value of f(x,y,z)=(x*y*z)^2 subject to
the constraint x^2+y^2+z^2=c^2, where c is not equal to zero.

2. Dec 18, 2003

### HallsofIvy

Staff Emeritus
Why is this not in the homework section?

Presuming they are homework, show us what you have done on these problems.