Implicit Function Homework: Finding Min/Max

[asi123]

Homework Statement

Hey.
I have this problem with the second part of the question.
In the first part, I needed to find all the extrema points of this implicit function and the second one is to find if it's minimum or maximum.
I posted only the derivative of the implicit function and the points I found.
BTW there was another condition to find the point, they said F(a) = b, so together with the derivative, I found the points.
Back to the question, as I was saying, the second part is to find if it's minimum or maximum, how do I do that?
I thought about finding the second derivative and plugging the points into it, but how do you find the second derivative of an implicit function, same as you find the first one?

I didn't posted the question, cause it's kind hard to translate, so I hope I gave you all the info you need.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Use the second derivative test: If y"(x)>0 x is a minimum, if y"(x)< 0 x is a maximum.