Finding the Global Maximum/Minimum of a function

**1. The problem statement, all variables and given/known data**

max f(x, y) = 2xy + 2y − x^2 − 2y^2

I need to get the value of x and y and determine if it gives the global maximum by using the infinity approach only.

Boundary is Negative infinity and Positive infinity

**2. Relevant equations**

max f(x, y) = 2xy + 2y − x^2 − 2y^2

**3. The attempt at a solution**

I am aware of the first step:

Partial differentiate with respect to x ++++++ 2y − 2x = 0

Partial differentiate with respect to y ++++++ 2x+ 2− 4y = 0

Solving both the equations will give x = y = 1

From here, I do not know how to use f(±INFINITY,±INFINITY) to determine if x = y = 1 yields the global maximum.

Your help is greatly appreciated. I have an exam next week on this.

Thanks,

Rye.