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Stewart_Calc_7ET ch14sec07
MULTIPLE CHOICE
1. Find the direction in which the maximum rate of change of f at the given point occurs.
a.
b.
c.
d.
e.
2. At what point is the following function a local minimum?
a.
b.
c.
d.
e.
3. Find the critical points of the function.
a.
b.
c.
d.
e.
4. Find and classify the relative extrema and saddle points of the function
for and .
a.
None
b.
Relative maximum
c.
Saddle point
d.
Relative minimum
5. Find the absolute extrema of the function
on the closed triangular region with vertices , and .
a.
Absolute minimum 0, Absolute maximum 5
b.
Absolute minimum –5, Absolute maximum 5
c.
Absolute minimum –5, Absolute maximum 17
d.
Absolute minimum 5, Absolute maximum 17
6. Suppose (1, 1) is a critical point of a function f with continuous second derivatives.
In the case of , , what can you say about f ?
a.
f has a local maximum at (1,1)
b.
f has a saddle point at (1,1)
c.
f has a local minimum at (1,1)
7. At what point is the following function a local maximum?
a.
b.
c.
d.
e.
8. Find all the saddle points of the function.
a.
b.
c.
d.
e.
9. Find the absolute minimum value of the function
on the set D. D is the region bounded by the parabola and the line
a.
b.
c.
d.
30
e.
0
10. Find the points on the surface that are closest to the origin.
a.
b.
c.
d.
e.
11. Find the dimensions of the rectangular box with largest volume if the total surface area is
given as .
a.
cm, 1.75 cm, 1.75 cm
b.
cm, cm, 1.75 cm
c.
cm, cm, cm
d.
cm, cm, cm
e.
cm, cm, 3.5 cm
12. Find the dimensions of a rectangular box of maximum volume such that the sum of the
lengths of its 12 edges is
a.
, ,
b.
4, 8, 16
c.
, ,
d.
32, , 16
e.
32, 32, 32
13. Find the shortest distance from the point to the plane .
a.
b.
c.
d.
e.
14. Find three positive numbers whose sum is and whose product is a maximum.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the local maximum, and minimum value and saddle points of the function.
2. A cardboard box without a lid is to have a volume of cm . Find the dimensions that
minimize the amount of cardboard used.
3. Find three positive numbers whose sum is and whose product is a maximum.
4. Find the maximum rate of change of f at the given point.
SHORT ANSWER
1. Find and classify the relative extrema and saddle points of the function
.
2. Find the absolute extrema of the function on the region
bounded by the disk defined by .
3. Find three positive real numbers whose sum is 388 and whose product is as large as
possible.
