Problem 2
Find the locations and values for the maximum and minimum of f(x, y) = 3x^3 ? 2x^2 + y^2 over the region given by x^2 + y^2 ?1.
and then over the region x^2 + 2y^2 ? 1.
Use the outline:
INSIDE
Critical points inside the region.
BOUNDARY
For each part of the boundary you should have:
• The function g(x, y) and ?g
• The equation ?f = ??g
• The set of three equations in three unknowns and their completesolution set
• The list of endpoints of that boundary component (ifnecessary)
COMPARE
Finally, you compute the value of f(x,y) at each point you haveidentified and compare to find the minimum and maximum.
Please show all steps for a thumbs up, thank you!
