Consider the function f (x, y) = x^2+ 4y^2 restricted to the domain x^2 + y^2 ≤ 1. This function has a single critical point at (0, 0). (a) Using an appropriate parameterization of the boundary of the...

 Consider the function f (x, y) = x^2+ 4y^2 restricted to the domain x^2 + y^2 ≤ 1. This function has a single critical point at (0, 0).
(a) Using an appropriate parameterization of the boundary of the domain, find the critical points of f(x,y) restricted to the boundary.
(b) Using the method of Lagrange Multipliers, find the critical points of f(x,y) restricted to the boundary.
(c) Assuming that the critical points you found were (±1, 0) and (0, ±1), find the absolute maximum and minimum
of f(x,y) restricted to this domain.