MAAATH

MTH 135 Participation Exercises for Week 5

Name___________________________________ Date: _________________________

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

Provide an appropriate response.

1) The critical values of f(x) = 4 - 48x + 24 are x = -2 and x = 2. Use the first derivative test to determine which of the

critical values correspond to a local maximum. 1) _______

A) x = 0 and x = 2 B) x = - 2 C) x = 2 and x = - 2 D) x = 2

2) Given f(x) = x + , x < 0, find the values of x corresponding to local maxima and local minima. 2) _______

A) local maximum at x = -4, local minimum at x = 4

B) local maximum at x = -4 (no local minimum)

C) no local maximum or minimum

D) local minimum at x = -4 (no local maximum)

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

3)

3) _______

A) (x) > 0 on (-∞, -6] ∪ [6, ∞), (x) < 0 on [-6, 6]

B) (x) > 0 on [-36, 36], (x) < 0 on (-∞, -36] ∪ [36, ∞)

C) (x) > 0 on (-∞, 6], (x) < 0 on [6, ∞)

D) (x) > 0 on [ -6, 6], (x) < 0 on (-∞, -6] ∪ [6, ∞)

Provide an appropriate response.

4) Find the critical values and determine the intervals where f(x) is decreasing for 4) _______

A) f(x) is decreasing on (-∞, 6); increasing on (6, ∞)

B) f(x) is decreasing on (-∞, 4); increasing on (4, ∞)

C) f(x) is decreasing on (-∞, -4); increasing on (-4, ∞)

D) f(x) is increasing on (-∞, 4); decreasing on (4, ∞)

Sketch a graph of the function.

5) f(x) = - 2 + 5

5) _______

A)

B)

C)

D)

Solve the problem.

6) The cost of manufacturing x electric woks in one day is given by C(x) = 2 -16 + 4x. Find the average cost per

electric wok and the interval where the average cost per electric wok is decreasing. 6) _______

A) (x) = 2 - 16x + 4; 0 < x < 4 B) (x) = 6 - 32x + 4; x < 4

C) (x) = 6 - 32x + 4; 0 < x < 4 D) (x) = 2 - 32x + 4; 0 < x < 4

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

7) f''(x) < 0

7) _______

A) (1, ∞) B) (-∞, -1) C) (-1, 0) , (1, ∞) D) (-1, 0)

Provide an appropriate response.

8) Find y'' for y = - 8) _______

A) 12 - B) + C) 4 - D) 4 +

9) Find the inflection point(s) for f(x) = - + 6. 9) _______

A) (0, 0) and (2, 2) B) (0, 6) and (2, 2) C) (0, 0) D) (0, 6) and (2, -4)

Solve the problem.

10) Because of material shortages, it is increasingly expensive to produce 6.2L diesel engines. In fact, the profit in millions

of dollars from producing x hundred thousand engines is approximated by where

Find the inflection point of this function to determine the point of diminishing returns. 10) ______

A) (10, 1958) B) (7.50, 2048) C) (10, 2048) D) (10, 114.67)

Provide an appropriate response.

11) Find vertical asymptotes for f(x) = . 11) ______

A) x = -1, x = -4 B) x = -1, x = 4 C) x = 1, x = -4 D) x = 1, x = 4

Find the limit, if it exists.

12) Find . 12) ______

A) 0 B) - ∞ C) ∞ D) 1

Find the domain and intercepts.

13) g(x) = 13) ______

A) Domain: All real numbers except 9; y intercept: 0; x intercept: 0

B) Domain: (-∞, -9); y intercept: 0; x intercept: 0

C) Domain: All real numbers except -9; y intercept: 0; no x intercept

D) Domain: All real numbers except -9; y intercept: 0; x intercept: 0

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

Provide an appropriate response.

14) Sketch the graph of Include sketch of all asymptotes. 14) _____________

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

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

f(x) = 5 - 15) ______

A) Relative maximum: (5, ) B) Relative maximum: (0, 5)

C) Relative minimum: (0, 5) D) Relative minima: (- , 0); ( , 0)

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 maximum: (0, 0)

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

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

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

17) The percent of concentration of a acid absorbed in a new manufacturing process after after the acid has been

mixed is given by A(x) = How long after the acid has been added is the concentration a maximum? Round

answer to the nearest tenth, if necessary. 17) ______

A) 4.9 hr B) 2.5 hr C) 7 hr D) 4 hr

Solve the problem.

18) A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it

is wide. Find the width of the box that can be produced using the minimum amount of material. Round to the nearest

tenth, if necessary. 18) ______

A) 6.4 ft B) 3.2 ft C) 7.2 ft D) 3.6 ft

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

19) The financial analysis department of a software design company determined that the cost of producing x palm

assistants is The department also determined the associated price-demand equation to be

where p is price in dollars.

a) Obtain the profit function. 19a _________________

b) Determine the maximum profit. 19b) ________________

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

20) A local office supply store has an annual demand for 50,000 cases of photocopier paper per year. It costs per year

to store a case of photocopier paper, and it costs to place an order. Find the optimum number of cases of photocopier

paper per order. 20) ____________

A) 1,581 cases B) 5,000,000 cases C) 707 cases D) 2,236 cases