Assignment:
Q1. Given f(x,y) = x^2-4xy+y^3+4y
Find the critical points and then use the Saddle Point Derivative Test to determine if they are max, min, or saddle points.
Q2. Given f(x,y)=4xy-x^4-y^4
Find the critical points and then use the Saddle Point Derivative Test to determine if they are max, min or saddle points.
Q3. Find the volume of the solid bounded above by z=x^2 and abounded below by the region enclosed by y=2-x^2 and y=x.
Q4. Find the volume of the solid in the first octant bounded by the coordinate planes z=4-y^2 and the plane x=3.
Q5. Find the volume of the wedge cut from the first octant by the cylinder
z=12-3y^2 and the plane x+y=2.
Provide complete and step by step solution for the question and show calculations and use formulas.