Larson_Calculus_10e ch03sec01
MULTIPLE CHOICE
1. Find the value of the derivative (if it exists) of the function at the extremum point
.
a.
b.
c.
d.
0
e.
1
2. Find the value of the derivative (if it exists) of at the indicated extremum.
a.
is undefined.
b.
c.
d.
e.
3. Find the value of the derivative (if it exists) of the function at the extremum point
.
a.
b.
0
c.
d.
e.
does not exist
4. Find all critical numbers of the function .
a.
critical numbers:
b.
critical numbers:
c.
critical numbers:
d.
critical numbers:
e.
no critical numbers
5. Find any critical numbers of the function .
a.
0
b.
c.
d.
e.
6. Find all critical numbers of the function , .
a.
b.
c.
d.
e.
7. Find all critical numbers of of the function , .
a.
b.
c.
d.
e.
8. Locate the absolute extrema of the function on the closed interval .
a.
absolute maximum:
absolute minimum:
b.
absolute maximum:
absolute minimum:
c.
absolute maximum:
absolute minimum:
d.
absolute maximum:
absolute minimum:
e.
absolute maximum:
absolute minimum:
9. Locate the absolute extrema of the function on the closed interval .
a.
absolute max: ; no absolute min
b.
no absolute max or min
c.
no absolute max; absolute min:
d.
absolute max: ; absolute min:
e.
absolute max: ; absolute min:
10. Locate the absolute extrema of the function on the closed interval .
a.
absolute max: ; absolute min:
b.
no absolute max; absolute min:
c.
absolute max: ; absolute min:
d.
absolute max: ; no absolute min
e.
no absolute max or min
11. Locate the absolute extrema of the function on the closed interval .
a.
The absolute maximum is , and it occurs at the critical number x = 0.
The absolute minimum is , and it occurs at the left endpoint .
b.
The absolute maximum is , and it occurs at either endpoint .
The absolute minimum is 0, and it occurs at the critical number x = 0.
c.
The absolute maximum is , and it occurs only at the left endpoint .
The absolute minimum is 0 and it occurs at the critical number x = 0.
d.
The absolute maximum is , and it occurs at the critical number x = 0.
The absolute minimum is , and it occurs at the right endpoint .
e.
The absolute maximum is , and it occurs only at the right endpoint
The absolute minimum is 0 and it occurs at the critical number x = 0.
12. Locate the absolute extrema of the given function on the closed interval .
a.
absolute max: (0, 0); absolute min
b.
absolute max: ; absolute min (0, 0)
c.
absolute max: ; absolute min
d.
absolute max: ; no absolute min
e.
no absolute max; absolute min:
13. Locate the absolute extrema of the function on the closed interval .
a.
absolute max: (0,1) ; absolute min:
b.
absolute max: ; absolute min: (0, 1)
c.
absolute max: ; no absolute min
d.
no absolute max; absolute min: (0, 1)
e.
absolute max: (0,1); no absolute min
14. Locate the absolute extrema of the function on the closed interval .
a.
The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
b.
The absolute is , and it occurs at the right endpoint .
The absolute is , and it occurs at the left endpoint .
c.
The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
d.
The absolute is , and it occurs at the right endpoint .
The absolute is and it occurs at the left endpoint .
e.
The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
15. Use a graphing utility to graph the function and locate the absolute extrema of the
function on the interval .
a.
absolute minimum:
no absolute maximum
b.
absolute minimum:
no absolute maximum
c.
absolute minimum:
no absolute maximum
d.
absolute minimum:
absolute maximum:
e.
absolute maximum:
absolute minimum:
16. Use a graphing utility to graph the function and locate the absolute extrema of the
function on the interval .
a.
left endpoint: absolute minimum
right endpoint: absolute maximum
critical points: none
b.
left endpoint: absolute minimum
right endpoint: absolute maximum
critical points: none
c.
left endpoint: absolute minimum
right endpoint:
critical points: absolute maximum
d.
left endpoint: absolute maximum
right endpoint: absolute minimum
critical points: none
e.
left endpoint: absolute minimum
right endpoint: absolute maximum
critical points:
17. Use a computer algebra system to graph the function and determine all absolute extrema
on the interval .
a.
absolute maximum:
absolute minimum:
b.
absolute maximum:
absolute minimum:
c.
absolute maximum:
absolute minimum:
d.
absolute maximum:
absolute minimum:
e.
absolute maximum:
absolute minimum:
18. The formula for the power output of battery is where is the electromotive force in
volts, is the resistance, and is the current. Find the current (measured in amperes) that
corresponds to a maximum value of P in a battery for which volts and ohm. Assume
that a -ampere fuse bounds the output in the interval . Round your answer to two decimal
places.
a.
amperes
b.
amperes
c.
amperes
d.
amperes
e.
amperes