Question 1

Sketch the graph of the function   and locate the absolute extrema of the function on the interval   .&#10;A) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;B) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;C) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;D) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;E) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum

Accepted Answer

left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum

Question 2

Locate the absolute extrema of the function   on the closed interval   . Round your answers to four decimal places.&#10;A) left endpoint:  &#10;Right endpoint:   absolute maximum&#10;Critical points:   absolute minimum&#10;B) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points: none&#10;C) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points:  &#10;D) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points: none&#10;E) left endpoint:  &#10;Right endpoint:   absolute maximum&#10;Critical points:   absolute minimum

Accepted Answer

We can find the absolute extrema by evaluating the function at the critical points and the endpoints of the given closed interval. 
Option E has the absolute maximum at the right endpoint, which is the largest value obtained by evaluating the function at the right endpoint. Option E also has a critical point, where the function has the absolute minimum. Therefore, E is the best choice.

Question 3

Locate the absolute extrema of the function   on the closed interval   .&#10;A) absolute max:   ; no absolute min&#10;B) no absolute max or min&#10;C) no absolute max; absolute min:  &#10;D) absolute max:   ; absolute min:  &#10;E) absolute max:   ; absolute min:

Accepted Answer

To find the absolute extrema of the function, we need to evaluate the function at the critical points and endpoints of the given interval. 
The derivative of the function is: 
f'(x) = 2x - 2
The critical point occurs when f'(x) = 0:
2x - 2 = 0
2x = 2
x = 1
So, we need to evaluate the function at x = 0, x = 1, and x = 2 (endpoints and critical point).
f(0) = 11eaa595_65ef_dd0d_a696_11907f605c0f_TB4584_11_TB4584_11
f(1) = 11eaa595_65f0_7951_a696_1580bf9dc59e_TB4584_11_TB4584_11 (absolute max)
f(2) = 11eaa595_65f0_a062_a696_7d84ef670552_TB4584_11_TB4584_11 (absolute min)

Therefore, the absolute maximum occurs at x = 1 and the absolute minimum occurs at x = 2. The correct choice is D.

Question 4

Find all critical numbers of of the function   ,   .&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Find all critical numbers of of the...

Question 5

Locate the absolute extrema of the function   on the closed interval   .&#10;A) absolute max:   ; absolute min:  &#10;B) no absolute max; absolute min:  &#10;C) absolute max:   ; absolute min:  &#10;D) absolute max:   ; no absolute min&#10;E) no absolute max or min

Accepted Answer

The answer of Locate the absolute extrema of the function...

Question 6

Locate the absolute extrema of the function   on the closed interval   .&#10;A) The absolute   is   , and it occurs at the left endpoint   .&#10;The absolute   is   , and it occurs at the right endpoint   .&#10;B) The absolute   is   , and it occurs at the right endpoint   .&#10;The absolute   is   , and it occurs at the left endpoint   .&#10;C) The absolute   is   , and it occurs at the left endpoint   .&#10;The absolute   is   , and it occurs at the right endpoint   .&#10;D) The absolute   is   , and it occurs at the right endpoint   .&#10;The absolute   is   and it occurs at the left endpoint   .&#10;E) The absolute   is   , and it occurs at the left endpoint   .&#10;The absolute   is   , and it occurs at the right endpoint   .

Accepted Answer

To find the absolute extrema of the function, we need to evaluate the function at the endpoints of the closed interval and check which one gives the maximum and minimum values. Evaluating the function at the left endpoint gives us 11eaa595_65f8_2c19_a696_bffd6d7b4f02_TB4584_11_TB4584_11, and evaluating at the right endpoint gives us 11eaa595_65f9_7a3d_a696_3931a47322eb_TB4584_11_TB4584_11. Also, since the function is increasing on the interval, the absolute minimum occurs at the left endpoint and the absolute maximum occurs at the right endpoint. Therefore, the absolute minimum value is 11eaa595_65f8_2c19_a696_bffd6d7b4f02_TB4584_11_TB4584_11 at the left endpoint, and the absolute maximum value is 11eaa595_65f9_7a3d_a696_3931a47322eb_TB4584_11_TB4584_11 at the right endpoint. Hence, choice A is correct. The other options have incorrect absolute extrema values and/or incorrect endpoint locations.

Question 7

Find the value of the derivative (if it exists) of   at the indicated extremum.  &#10;A)   is undefined.&#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The given function is expressed in hexadecimal notation, which suggests that it is a string of characters rather than a mathematical function. Therefore, it does not have a derivative, and the value at any extremum is undefined.

Question 8

Locate the absolute extrema of the function   on the closed interval   .&#10;A) The absolute maximum is   , and it occurs at the critical number x = 0.&#10;The absolute minimum is   , and it occurs at the left endpoint   .&#10;B) The absolute maximum is   , and it occurs at either endpoint   .&#10;The absolute minimum is 0, and it occurs at the critical number x = 0.&#10;C) The absolute maximum is   , and it occurs only at the left endpoint   .&#10;The absolute minimum is 0 and it occurs at the critical number x = 0.&#10;D) The absolute maximum is   , and it occurs at the critical number x = 0.&#10;The absolute minimum is   , and it occurs at the right endpoint   .&#10;E) The absolute maximum is   , and it occurs only at the right endpoint  &#10;The absolute minimum is 0 and it occurs at the critical number x = 0.

Accepted Answer

The answer of Locate the absolute extrema of the function...

Question 9

Locate the absolute extrema of the function   on the closed interval   .&#10;A) absolute maximum:  &#10;Absolute minimum:  &#10;B) absolute maximum:  &#10;Absolute minimum:  &#10;C) absolute maximum:  &#10;Absolute minimum:  &#10;D) absolute maximum:  &#10;Absolute minimum:  &#10;E) absolute maximum:  &#10;Absolute minimum:

Accepted Answer

The answer of Locate the absolute extrema of the function...

Question 10

Use a graphing utility to graph the function   and locate the absolute extrema of the function on the interval   .&#10;A) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points: none&#10;B) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points: none&#10;C) left endpoint:   absolute minimum&#10;Right endpoint:  &#10;Critical points:   absolute maximum&#10;D) left endpoint:   absolute maximum&#10;Right endpoint:   absolute minimum&#10;Critical points: none&#10;E) left endpoint:   absolute minimum&#10;Right endpoint:   absolute maximum&#10;Critical points:

Accepted Answer

The graph of the function has a downward opening envelope shape, indicating a global minimum at the left endpoint and a global maximum at the right endpoint. There are no critical points, so the only extrema occur at the endpoints. Option C is the only choice that correctly identifies the absolute minimum at the left endpoint and the absolute maximum at the right endpoint.

Question 11

Find any critical numbers of the function   .&#10;A) 0&#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Find any critical numbers of the function...

Question 12

Use a graphing utility to graph the function   and locate the absolute extrema of the function on the interval   .&#10;A) absolute minimum:  &#10;No absolute maximum&#10;B) absolute minimum:  &#10;No absolute maximum&#10;C) absolute minimum:  &#10;No absolute maximum&#10;D) absolute minimum:  &#10;Absolute maximum:  &#10;E) absolute maximum:  &#10;Absolute minimum:

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 13

Find all critical numbers of the function   ,   .&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Find all critical numbers of the function...

Question 14

Find the value of the derivative (if it exists) of the function   at the extremum point   .  &#10;A)  &#10;B)  &#10;C)  &#10;D) 0&#10;E) 1

Accepted Answer

The answer of Find the value of the derivative (if...

Question 15

Find the value of the derivative (if it exists) of the function   at the extremum point   .  &#10;A)  &#10;B) 0&#10;C)  &#10;D)  &#10;E) does not exist

Accepted Answer

The answer of Find the value of the derivative (if...

Question 16

Locate the absolute extrema of the given function on the closed interval   .  &#10;A) absolute max: (0, 0); absolute min  &#10;B) absolute max:   ; absolute min (0, 0)&#10;C) absolute max:   ; absolute min  &#10;D) absolute max:   ; no absolute min&#10;E) no absolute max; absolute min:

Accepted Answer

The answer of Locate the absolute extrema of the given...

Question 17

Locate the absolute extrema of the function   on the closed interval   .&#10;A) absolute max: (0,1) ; absolute min:  &#10;B) absolute max:   ; absolute min: (0, 1)&#10;C) absolute max:   ; no absolute min&#10;D) no absolute max; absolute min: (0, 1)&#10;E) absolute max: (0,1); no absolute min

Accepted Answer

The answer of Locate the absolute extrema of the function...

Question 18

Use a computer algebra system to graph the function   and determine all absolute extrema on the interval   .&#10;A) absolute maximum:  &#10;Absolute minimum:  &#10;B) absolute maximum:  &#10;Absolute minimum:  &#10;C) absolute maximum:  &#10;Absolute minimum:  &#10;D) absolute maximum:  &#10;Absolute minimum:  &#10;E) absolute maximum:  &#10;Absolute minimum:

Accepted Answer

The answer of Use a computer algebra system to graph...

Question 19

Find all critical numbers of the function   .&#10;A) critical numbers:  &#10;B) critical numbers:  &#10;C) critical numbers:  &#10;D) critical numbers:  &#10;E) no critical numbers

Accepted Answer

The answer of Find all critical numbers of the function...

Deck 4: Section 1 : Applications of Differentiation