MATH1910Chapter3Section1Homework

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Multiple Choice
Identify the choice that best completes the statement or answers the question.

Find the value of the derivative (if it exists) of the function

at the extremum point

a.
b.
c.
d.	0
e.	1

Find the value of the derivative (if it exists) of

at the indicated extremum.

a.	is undefined.
b.
c.
d.
e.

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

Find all critical numbers of the function

a.	critical numbers:
b.	critical numbers:
c.	critical numbers:
d.	critical numbers:
e.	no critical numbers

Find any critical numbers of the function

a.	0
b.
c.
d.
e.

Find all critical numbers of the function

a.
b.
c.
d.
e.

Find all critical numbers of of the function

a.
b.
c.
d.
e.

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:

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.

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