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Step 1 : \ \

Second partials test : \ \

If f  have continuous partial derivatives on an open region containing a point for which   

and .

To test for relative extrema of f , consider the quantity

1. If and , then f  has a relative minimum at .

2. If and , then f  has a relative maximum at .

3. If and , then is a saddle point. 

4. The test is inconclusive if .  

Step 2 : 

The function is .

Apply partial derivative on each side with respect to x.

Differentiate partially with respect to x.

Differentiate partially with respect to y.

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Step 3 :  \ \

The function is .

Apply partial derivative on each side with respect to y

Differentiate partially with respect to y.

Differentiate partially with respect to x.

   \ \

Step 4 : \ \

Find the critical points :

Equate   to zero.

Equate to zero.

The critical point is .

\

Find the quantity d :

Since and , the function f  has a relative maximum at .

Substitute the point in .

The function has relative maximum at  . \ \

Solution : \ \

The function has relative maximum at  .