Maximum and Minimum Values.htm

Maximum and Minimum Values: Examples

1. Find the and describe the critical point(s) for the following function:

Answer:

First find the critical points, this is done by finding the x and y partial derivatives, and setting them equal to zero then solving as a system:

Solve the system:

Then, test the point (-2,3) and you will find that . Testing other points around it shows that the point is lower than other

around it, which means that it is a minimum.

2.Find the extrema of the following function:

Answer:

Finding the critical points in the same way as above, we find that they are: (0,0) and (). Now we use the second derivative test.

First we find $f_{xx}$ , $f_{yy},f_{xy}.$ These are shown below:

Now using the second derivative test formula, we check each of the points:

We find the following:

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