Quiz (Extrema of Functions of Several Variables)

Show all work and justify each step.

(1) Find the critical points and classify each as a relative maximum, a relative minimum, or a saddle point for each given function.

    (a)

    (b)

    (c)

    (d)

    (e)

    (f)

(2) Find the absolute maximum and minimum values of the given functions over the given region.

    (a) on the disk

    (b) on the disk

    (c) on the square

(3) Find three positive numbers whose sum is 54 and whose product is as large as possible.

(4)  Let be the triangular region in the -plane with vertices and A plate in the shape of is heated so that the temperature at is



(in degrees Celsius). At what point in or on its boundary is maximized? What are the temperatures?

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Extrema Of Functions Of Several Variables Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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