Solve Highest/Lowest Points on Curve of Intersection with Lagrange Multipliers

[Cherizzle]

Hi There I would like help on a question about Lagrange multipliers.

Question: Consider the intersection of two surfaces: an elliptic paraboloid z=x^2 + 2*x + 4*y^2 and a right circular cylinder x^2 + y^2 = 1. Use Lagrange multipliers to find the highest and lowest points on the curve of the intersection.

What I have so far:
I managed to find my critical points using lagrange multipliers. But now I don't know how to describe whether my points are at maximum or minimum...
The points I found were: (2/3, -$$\sqrt{5}$$/3) and (-$$\sqrt{2}$$/6, 1)

 

[uart]

Hi Cherizzle. Are you sure that's supposed to be z=x^2 + 2*x + 4*y^2 and not z=x^2 + 2*x*y + 4*y^2