# Calculus 3 : Absolute Minimums and Maximums

## Example Questions

### Example Question #1 : Absolute Minimums And Maximums

Find the absolute minimums and maximums of on the disk of radius  .

Absolute Minimum: Absolute Maximum:  Absolute Minimum: Absolute Maximum: Absolute Minimum: Absolute Maximum:  Absolute Minimum: Absolute Maximum: Absolute Minimum: Absolute Maximum: Absolute Minimum: Absolute Maximum:  Explanation:

The first thing we need to do is find the partial derivative in respect to , and .  We need to find the critical points, so we set each of the partials equal to .  We only have one critical point at , now we need to find the function value in order to see if it is inside or outside the disk. This is within our disk.

We now need to take a look at the boundary, . We can solve for , and plug it into .   We will need to find the absolute extrema of this function on the range . We need to find the critical points of this function.  The function value at the critical points and end points are:   Now we need to figure out the values of these correspond to.   Now lets summarize our results as follows:    From this we can conclude that there is an absolute minimum at , and two absolute maximums at and .

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