MTH 135 Homework Assignment for Week 5

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Use the first derivative test to determine the local extrema, if any, for the function:

1) _______

A) local max at B) local max at x = 2 and local min at – 4

C) local max at and local min at D) local min at

2) Use the first derivative test to determine the local extrema, if any, for the function:

2) _______

A) local min at and local max at

B) local max at and local min at

C) local max at x = 1 and local min at x = 0

D) local max at and local min at

Use the given graph of f(x) to find the intervals on which (x) > 0.

3)

3) _______

A) (x) < 0 on (-∞,∞)

B) (x) > 0 on (-∞, -3] ∪ [ 1, ∞), (x) < 0 on [-3, 1]

C) (x) > 0 on [-3, ∞), (x) < 0 on (-∞, -3]

D) (x) > 0 on [-1, ∞), (x) < 0 on decreasing on (-∞, -1]

Provide an appropriate response.

4) Find the critical values and determine the intervals where f(x) is increasing and f(x) is decreasing if

4) _______

A) increasing on ; decreasing on and (0, ∞)

B) increasing on (-4, 0); decreasing on (-∞, -4) and (0, ∞)

C) decreasing on ; increasing on and (0, ∞)

D) decreasing on (-4, 0); increasing on (-∞, -4) and (0, ∞)

Sketch a graph of the function.

5) f(x) = 3 – 12

5) _______

A)

B)

C)

D)

Solve the problem.

6) The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately

and , where x denotes the number of clocks made. What is the maximum annual profit?

6) _______

A) $ 753,333 B) $ 853,333 C) $ 653,333 D) $ 553,333

Find the intervals where f”(x) < 0 ir f”(x) > 0 as indicated.

7) f”(x) < 0

7) _______

A) (-2, ∞) B) (-5, 2) C) (-∞, -2) D) (-5, 5)

Provide an appropriate response.

8) Find y” for y = . 8) _______

A) y” = – B) y” = –

C) y” = D) y” = –

9) Find y” for y = 2 – 6 . 9) _______

A) y” = 3 – 3 B) y” = 3 + 3

C) y” = + D) y” = +

10) Find the inflection point(s) for f(x) = . 10) ______

A) (-6, 1) B) (-3, 2)

C) (-7, 0) D) There are no points of inflection.

Solve the problem.

11) A company estimates that it will sell N(t) hair dryers after spending $t thousands on advertising as given by:

N(t) = -3 + 450 – 21,600t + 1,100, 40 ≤ t ≤ 60

For which values of t is the rate of sales N'(t) increasing? 11) ______

A) 40 < t < 50 B) 50 < t < 60 C) t > 40 D) 40 < t < 60

Provide an appropriate response.

12) Find horizontal asymptotes, if any, for f(x) = . 12) ______

A) y = B) y = – C) y = 0 D) y =

Find the domain and intercepts.

13) f(x) = 4x + 8 13) ______

A) Domain: (-∞, ∞); y intercept: -2; x intercept: 8

B) Domain: (-∞, ∞); y intercept: 8; x intercept: -2

C) Domain: (-2, ∞); y intercept: 8; x intercept: -2

D) Domain: (-∞, ∞); y intercept: 8; x intercept: 2

Find the limit, if it exists.

14) Find . 14) ______

A) – ∞ B) 0 C) D) ∞

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

15) Sketch the graph of Include sketch of all asymptotes. 15) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

16) Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

f(x) = 20 – 3 16) ______

A) Relative minimum: (-2 , -64) Relative minimum: (0, 0) Relative maximum: (2 , 64)

B) Relative minimum: (-2 , -64) Relative maximum: (2 , 64)

C) Relative maximum: (0, 0) Relative minimum: (2, 64)

D) Relative minimum: (-2, -64) Relative maximum: (0, 0)

17) Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

f(x) = 17) ______

A) Relative maximum: (0, 8) B) Relative maximum: (0, -8)

C) Relative maximum: (-1, 8) D) No relative extrema

18) A drug that stimulates reproduction is introduced into a colony of bacteria. After t minutes, the number of bacteria is

given approximately by:

N(t) = 1,000 + 36 – , 0 ≤ t ≤ 30

At what value of t is the number of bacteria a maximum? 18) ______

A) 30 min B) 24 min C) 6 min D) 12 min

19) Find the absolute minimum value of f(x) = 5 + 4x + for x > 0. 19) ______

A) min f(x) = f(0) = 5 B) min f(x) = f(1) = 25 C) min f(x) = f(2) = 13 D) min f(x) = f(2) = 21

Solve the problem.

20) A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance

around) does not exceed 102 in. What dimensions will give a box with a square end the largest possible volume?

20) ______

A) 17 in. × 17 in. × 85 in. B) 17 in. × 17 in. × 34 in.

C) 17 in. × 34 in. × 34 in. D) 34 in. × 34 in. × 34 in.

21) The annual revenue and cost functions for a manufacturer of zip drives are approximately and

, where x denotes the number of drives made. What is the maximum annual profit? 21) ______

A) $1,520,000 B) $1,820,000 C) $1,620,000 D) $1,720,000

22) A bookstore has an annual demand for 63,000 copies of a best-selling book. It costs $0. 40 to store one copy for one

year, and it costs $ 125 to place an order. Find the optimum number of copies per order. 22) ______

A) 9,922 copies B) 8,099 copies C) 6,275 copies D) 5,648 copies