Fluent Essays

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 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