Finding max and min of x²y on the circle x²+y²=1

[chesshaha]

Homework Statement

find the max and min of f(x,y)=x^2y, constraint x^2+y^2=1

Homework Equations

None.

The Attempt at a Solution

I found that possible points use the procedure of the method of lagrange multiplier, I got $$(\pm\sqrt{2/3}, \pm\sqrt{1/3}$$ so 4 points total.
But do I have to check the end point on the constraint? like points (-1, 0), (1, 0), (0, 1), (0, -1)?and y this latex thing won't work? help please. lol

 

[Mindscrape]

You should check the boundaries because for 1) they could have max or min depending contexts and 2) they will give you some sanity towards the answer you have.

 

[sam1]

Change the direction of the slash on your closing tex tag. [\tex] sould be [ /tex] (witout the space obviously)