# y/x +2/y + x?

asked Mar 13, 2015 in CALCULUS

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.

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.

answered Mar 13, 2015
edited Mar 13, 2015 by sandy

contd...

Step 4 :

Find the critical points :

Equate to zero.

Equate to zero.

Substitute in the above equation

When , .

The critical point are and .

Step 5 :

Find the quantity of d .

The quantity of at .

Find at  .

Since  and , then f  has a relative maximum at .

The quantity of at .

Find  at .

If and , then f  has a relative minimum at .

Solution :

Relative maximum at .

Relative minimum at .

answered Mar 13, 2015