For each of the following functions, find the maximum and mimimum values of
the function on the circular disk:
. Do this by looking at the level curves and
gradiants.

(A) :
maximum value =
minimum value =

(B) :
maximum value =
minimum value =

(C) :
maximum value =
minimum value =

A)
maximum value = 2.414
minimum value = -0.414

B)
maximum value = 2
minimum value = 0

C)
maximum value = 1
minimum value = -2

The work

2.

Find the maximum and minimum values of
on the ellipse
maximum value:
minimum value:

Max: 7.0029
Min: -7.0028

The work

3.

Find the maximum and minimum values of
on the sphere
.
maximum value =
minimum value =

Max: 3.742
Min: -3.742

The work

4.

Find the maximum and minimum volumes of a rectangular box whose
surface area equals 4000 square cm and whose edge length (sum of
lengths of all edges) is 320 cm.
Hint: It can be deduced that the box is not a cube, so if x, y, and z
are the lengths of the sides, you may want to let x represent a side
with x ≠ y and x ≠ z.
Maximum value is ,
occuring at
(, ,).
Minimum value is ,
occuring at
(, ,).

Max: 16000 at ( 40, 20, 20)

Min: 14814.81 at ( 40/3, 100/3, 100/3)

The work

5.

The plane x + y + 2z = 20 intersects the paraboloid in an ellipse. Find the points on this ellipse that are
nearest to and farthest from the origin.
Point farthest away occurs at
(, ,).
Point nearest occurs at
(, ,).