Larson_Calculus_10e ch13sec08
MULTIPLE CHOICE
1. Identify any extrema of the function by recognizing its given form or its
form after completing the square.
a.
relative maximum:
b.
relative maximum:
c.
relative minimum:
d.
relative minimum:
e.
relative maximum:
2. Identify any extrema of the function by recognizing its given form or
its form after completing the square.
a.
relative maximum:
b.
relative minimum:
c.
relative minimum:
d.
relative maximum:
e.
relative maximum:
3. Examine the function for relative extrema.
a.
relative minimum:
b.
relative maximum:
c.
relative maximum:
d.
relative maximum:
e.
relative minimum:
4. Examine the function for relative extrema.
a.
relative minimum:
b.
relative maximum:
c.
relative minimum:
d.
relative minimum:
e.
relative maximum:
5. Examine the function for relative extrema.
a.
relative maximum:
b.
relative minimum:
c.
relative maximum:
d.
relative minimum:
e.
no relative extrema
6. Examine the function for relative extrema and saddle points.
a.
saddle point:
b.
relative minimum:
c.
relative minimum:
d.
saddle point:
e.
saddle point:
7. Examine the function for relative extrema and saddle points.
a.
relative minimum:
b.
relative minimum:
c.
relative maximum:
d.
saddle point:
e.
saddle point:
8. Examine the function for relative extrema and saddle points.
a.
saddle point: ; relative minimum:
b.
saddle point: ; relative minimum:
c.
relative minimum: ; relative maximum:
d.
relative minimum: ; relative maximum:
e.
saddle points: ,
9. Examine the function for relative extrema and saddle points.
a.
saddle point:
b.
relative minimum:
c.
relative maximum:
d.
relative minimum:
e.
no critical points
10. Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient
information to determine the nature of the function at the critical point , if
.
a.
relative maximum
b.
relative minimum
c.
saddle point
d.
insufficient information
11. List the critical points of the function for which the Second Partial Test
fails.
a.
Test fails at and .
b.
Test fails only at .
c.
Test fails at .
d.
Test fails at .
e.
Test fails only at .
12. Find the critical points of the function , and from the form
of the function, determine whether a relative maximum or a relative minimum occurs at each point.
a.
relative minimum at
b.
relative maximum at
c.
relative maximum at
d.
relative minimum at
e.
no relative extrema
13. Find the critical points of the function , and from the form of
the function, determine whether a relative maximum or a relative minimum occurs at each point.
a.
relative maxima at , , , where are arbitrary
real numbers
b.
relative minima at , , , where are arbitrary
real numbers
c.
relative minimum at
d.
relative maximum at
e.
no relative extrema
14. Find the absolute extrema of on the region bounded by the square with
vertices
a.
absolute minimum:
absolute maximum:
b.
absolute minimum:
absolute maximum:
c.
absolute minimum:
absolute maximum:
d.
absolute minimum:
absolute maximum:
e.
absolute minimum:
absolute maximum:
15. Find the absolute extrema of the function over the triangular region in the xy–
plane with vertices .
a.
absolute maximum: at
absolute minimum: at and along the line
b.
absolute maximum: at
absolute minimum: at and along the line
c.
absolute maximum: at
absolute minimum: at and along the line
d.
absolute maximum: at
absolute minimum: at
e.
absolute maximum: at
absolute minimum: at
16. Find the absolute extrema of on the region .
a.
absolute minimum:
absolute maximum:
b.
absolute minimum:
absolute maximum:
c.
absolute minimum:
absolute maximum:
d.
absolute minimum:
absolute maximum:
e.
absolute minimum:
absolute maximum: