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Find all points where the function has any relative extrema or saddle points and identify the type of relative extreme.

0 votes

y/x +2/y + x?

asked Mar 13, 2015 in CALCULUS by anonymous

2 Answers

0 votes

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 by sandy Pupil
edited Mar 13, 2015 by sandy
0 votes

contd...

Step 4 :

Find the critical points :

Equate to zero.

Equate to zero.

Substitute image in the above equation

When , .

The critical point are and .

Step 5 :

Find the quantity of d .

image

The quantity of at .

image

Find image at  .

image

Since  and , then f  has a relative maximum at .

The quantity of at .

image

Find  image at image.

image

If and , then f  has a relative minimum at .

Solution :

Relative maximum at .

Relative minimum at .

answered Mar 13, 2015 by sandy Pupil

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