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Examine the function for relative extrema and saddle points.

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Examine the function for relative extrema and saddle points.

g (x, y) = xy

asked Feb 18, 2015 in CALCULUS by anonymous

2 Answers

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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 , 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.

image

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.

image

answered Feb 20, 2015 by Thomas Apprentice
0 votes

Contd........

Step 4 :

Find the critical points :

Equate   to zero.

image

Equate to zero.

image

The critical point is image.

Find the quantity d :

image

Since , image is a saddle point.

Substitute the point image in .

image

The saddle point is image.

Solution :

The saddle point is image.

answered Feb 20, 2015 by Thomas Apprentice

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