Assignment 6. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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Duane Robbins
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1 Assinment 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Round your answer, if appropriate. 1) A man 6 ft tall walks at a rate of 3 ft/sec away from a lamppost that is 23 ft hih. At what rate is the 1) lenth of his shadow chanin when he is 70 ft away from the lamppost? (Do not round your answer) A) 35 ft/sec B) ft/sec C) ft/sec D) ft/sec Find the location of the indicated absolute extremum for the function. 2) Maximum 2) A) x = 0 B) No maximum C) x = -1 D) x = 2 Find all possible functions with the iven derivative. 3) y = 3t - 2 t 3) A) 3t2-2 t + C B) 3t 2-4 t + C C) 3 2 t 2-4 t + C D) t2-2 t + C Find the function with the iven derivative whose raph passes throuh the point P. 4) (x) = 4 + 6x, P(-1, 4) 4) x2 A) (x) = 4x-2 + 6x - 3 B) (x) = 4x2 + 3x2-3 C) (x) = -4x-1 + 3x2-3 D) (x) = -4x-1 + 3x2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Answer the question. 5) It took 29 seconds for the temperature to rise from 2 F to 118 F when a thermometer was 5) taken from a freezer and placed in boilin water. Althouh we do not have detailed knowlede about the rate of temperature increase, we can know for certain that, at some time, the temperature was increasin at a rate of 4 F/sec. Explain. 1

2 Give an appropriate answer. 6) Show that the function f(x) = x3 + 2 x2 + 5 has exactly one zero on the interval (-, 0). 6) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the iven interval. cos, - < 0 7) f( ) = 0, = 0 7) A) Yes B) No Find the value or values of c that satisfy the equation f(b) - f(a) = f'(c) b - a in the conclusion of the Mean Value Theorem for the iven function and interval. 8) f(x) = x2 + 4x + 2, [-3, -2]. 8) A) - 5 2, 5 2 B) 0, C) D) -3, -2 9) On our moon, the acceleration of ravity is 1.6 m/sec2. If a rock is dropped into a crevasse, how fast 9) will it be oin just before it hits bottom 45 seconds later? A) 3240 m/sec B) -72 m/sec C) -36 m/sec D) 72 m/sec 10) Given the acceleration, initial velocity, and initial position of a body movin alon a coordinate 10) line at time t, find the body's position at time t. a = 3.2, v(0) = -18, s(0) = -13 A) s = 3.2t2-18t - 13 B) s = 1.6t2-18t C) s = 1.6t2-18t - 13 D) s = -1.6t2 + 18t - 13 Find the value or values of c that satisfy the equation f(b) - f(a) = f'(c) b - a in the conclusion of the Mean Value Theorem for the iven function and interval. 11) f(x) = ln (x - 4), [5, 8] Round to the nearest thousanh. 11) A) B) C) ±6.164 D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Answer the question. 12) A marathoner ran the 26.2 mile New York City Marathon in 2.3 hrs. Did the runner ever 12) exceed a speed of 9 miles per hour? 2

3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the absolute extreme values of each function on the interval. 13) F(x) = - 3, 0.5 x 4 13) x2 A) Maximum = 4, ; minimum = 1 2, -12 B) Maximum = 4, ; minimum = - 1 2, -12 C) Maximum = 1 2, 3 16 ; minimum = (4, -12) D) Maximum = 1 2, ; minimum = (-4, -12) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 14) Consider the quartic function 14) f(x) = ax4 + bx3 + cx2 + dx + e, a 0. Must this function have at least one critical point? Give reasons for your answer. (Hint: Must f (x) = 0 for some x?) How many local extreme values can f have? Answer the problem. 15) Use the followin function and a raphin calculator to answer the questions. 15) f(x) = x4-4x2 + 3x + 3, [-0.5, 1.8] a). Plot the function over the interval to see its eneral behavior there. Sketch the raph below. b). Find the interior points where f = 0 (you may need to use the numerical equation solver to approximate a solution). You may wish to plot f as well. List the points as ordered pairs (x, y). 3

4 15) c). Find the interior points where f does not exist. List the points as ordered pairs (x, y). d). Evaluate the function at the endpoints and list these points as ordered pairs (x, y). e). Find the function's absolute extreme values on the interval and identify where they occur. 16) If the derivative of an even function f(x) is zero at x = c, can anythin be said about the 16) value of f at x = -c? Give reasons for your answer. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the location of the indicated absolute extremum for the function. 17) Maximum 17) A) x = -1 B) No maximum C) x = 1 D) x = 4 4

5 18) Maximum 18) A) No maximum B) x = 11 4 C) x = -4 D) x = 0 Find the extreme values of the function and where they occur. 19) y = x2e-x + 2xe-x 19) A) Minimum value is 2e 2 (1-2 ) at x = - 2; no maximum value. B) Maximum value is 2e- 2 (1 + 2 ) at x = ; no minimum value. C) Minimum value is 2e 2 (1-2 ) at x = - 2; maximum value is 2e- 2 (1 + 2 ) at x = 2. D) None Find the absolute extreme values of each function on the interval. 20) y = 6-7x2 on [-3, 4] 20) A) Maximum = (0, 12); minimum = (4, -57) B) Maximum = (0, 6); minimum = (4, -106) C) Maximum = (0, 42); minimum = (-3, -57) D) Maximum = (0, 7); minimum = (4, -118) Find the extreme values of the function and where they occur. 21) y = x3-3x ) A) Local minimum at (2, -3). B) None C) Local maximum at (0, 1), local minimum at (2, -3). D) Local maximum at (0, 1). Round your answer, if appropriate. 22) Water is bein drained from a container which has the shape of an inverted riht circular cone. The 22) container has a radius of 9.00 inches at the top and a heiht of 10.0 inches. At the instant when the water in the container is 9.00 inches deep, the surface level is fallin at a rate of 0.7 in./sec. Find the rate at which water is bein drained from the container. A) 113 in.3s B) 155 in.3/s C) 144 in.3/s D) 138 in.3/s 5

6 23) The rane R of a projectile is related to the initial velocity v and projection anle by the equation 23) R = v 2 sin 2, where is a constant. How is dr/ related to d / if v is constant? A) dr = v 2 cos 2 d C) dr = - v 2 cos 2 d B) dr = 2v 2 cos 2 d D) dr = 2v 2 sin 2 d Round your answer, if appropriate. 24) Boyle's law states that if the temperature of a as remains constant, then PV = c, where 24) P = pressure, V = volume, and c is a constant. Given a quantity of as at constant temperature, if V is decreasin at a rate of 9 in. 3/sec, at what rate is P increasin when P = 30 lb/in.2 and V = 20 in.3? (Do not round your answer.) A) 27 2 lb/in. 2 per sec B) lb/in. 2 per sec C) 9 4 lb/in. 2 per sec D) 6 lb/in.2 per sec 25) Water is fallin on a surface, wettin a circular area that is expandin at a rate of 6 mm2/s. How 25) fast is the radius of the wetted area expandin when the radius is 195 mm? (Round your answer to four decimal places.) A) mm/s B) mm/s C) mm/s D) mm/s 26) The rane R of a projectile is related to the initial velocity v and projection anle by the equation 26) R = v 2 sin 2, where is a constant. How is dr/ related to dv/ if is constant? A) dr = 2v dv C) dr = 2v 2 cos 2 dv B) dr D) dr = 2v cos 2 = 2v sin 2 dv dv 27) The volume of a square pyramid is related to the lenth of a side of the base s and the heiht h by 27) the formula V = 1 3 s 2h. How is dv/ related to ds/ if h is constant? A) dv = 2hs ds 3 B) dv = 2s ds 3 C) dv = s 2 ds 3 D) dv = h ds 3 6

7 Round your answer, if appropriate. 28) The volume of a sphere is increasin at a rate of 9 cm3/sec. Find the rate of chane of its surface 28) area when its volume is 32 cm3. (Do not round your answer.) 3 A) 18 cm2/sec B) 9 cm2/sec C) 8 3 cm 2/sec D) 6 cm2/sec 29) Assume that the profit enerated by a product is iven by P(x) = 2 x, where x is the number of 29) units sold. If the profit keeps chanin at a rate of $100 per month, then how fast are the sales chanin when the number of units sold is 1100? (Round your answer to the nearest dollar per month.) A) $13,266/month B) $1658/month C) $3317/month D) $3/month Round your answer, if appropriate. 30) The volume of a rectanular box with a square base remains constant at 800 cm3 as the area of the 30) base increases at a rate of 13 cm2/sec. Find the rate at which the heiht of the box is decreasin when each side of the base is 11 cm lon. (Do not round your answer.) A) cm/sec B) cm/sec C) cm/sec D) cm/sec 7

dollars for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred dollars) earned from t = 10 to t = 16?

dollars for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred dollars) earned from t = 10 to t = 16? MATH 7 RIOHONDO SPRING 7 TEST (TAKE HOME) DUE 5//7 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) A department store has revenue from the sale