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Chapter ll-Il ,student:Il:Date:2117117 1. lim F(x) x--+ - 2 lim F(x) x--+ - 5 2. Use the properties of ,2 -1o lim -------x-4 \-)4 3. Use the properties of limits to 5x Select the correct choice below and, if dA' *2 - 16 lim = x-4 x-4 lnstructor: Il whether the I What is the value of the limit? Select the correct choice below and fill in any answer boxes in your choice. A. tim F(x) = x--+ - 2 (Type an integer or a simplified fraction.) B. The limit does not exist. What is the value of the limit? Select the correct choice below and fill in any answer boxes in your choice. A. tim F(x) = x+-5 (Type an integer or a simplified fraction.) B. The limit does not exist. Decide from the graph whether each limit exists. lf a limit exists, estimate its value. Assignment: -iI) answer box within your choice. lf the limit exists, find its value. in the answer box within your choice. to help decide whether the limit exists. lf the exists, find its value. (Simplify your answer.) B- The limit does not and is neither oo nor ,.A ** Select the correct choice below and, if rA. 5x 5 lim 9--6 = g (Simplify your answer. an integer or a fraction.) I of 1l B. The limit does not exist and is neither co nor - oo Chapter tt-II YA.

B.

c.

D. 4. of the population of a cutture of tumor cetls is given by p(Q = # Select the choice below and fill in the answer box if #A. lim P(t) 3600 t--+m B. The limit exist. Choose the correct Find and interpret lim p(t), t-+ oo . The limit does not exist and is not oo or - oo. . The limit for the smaller value is . The limit does not exist and is not oo or - oo. 5. Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. *2 -64 r(x) = x_ o Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.) A. f is discontinuous at the two values x = . The limit for the smaller value is . The limit for the larger value does not exist and is not o or - oo. B. f is discontinuous over the interval (Type your answer in interval notation.) C. f is discontinuous over the interval (Type your answer in interval notation.) D. f is discontinuous at the two values x = . The limit for the larger value is E' f is discontinuous at the single value x = The number of tumor gets closer to 3600 as time increases. The number of cells closer to oo as time decreases. The nu tumor cells to 3600 as time decreases. of tumor cells gets closer to oo as time increases . The limit is F.

G. f is discontinuous at the single value x = f is discontinuous at the two values x = notrcor-oo- f is discontinuous at the two values x = and is not oo or - oo. The limit for the larger value is f is continuous for all values of x. . The limit is . The limit for both values do not exist and are . The limit for the smaller value does not exist H. 2of11 I-II Chapter l1-Il 12. Estimate the slope (slope = rise/run) of the tangent line to the curve. 13. What is your estimate of the slope? slope r 2 (Round to the nearest integer.) Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the derivative exists. f(x)= -12*5*-3 f'(x) = _ (Type an expression using x as the variable.) Select the corect answer below and, if necessary fill in the answer box to complete your choice. A. f,(1) = (Type an integer or a simplified fraction.) B. The derivative does not exist. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. f,(2) = (Type an integer or a simplified fraction.) B. The derivative does not exist. Select the correct ans\ffer below and, if necessary fill in the answer box to complete your choice. A. f,(3) = (Type an integer or a simplified fraction.) B. The derivative does not exist. For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y=f(x)=12 **; x= -4, x= -2 The equation of the secant line is y = 14. a.

b. 6 of ll The equation of the tangent line is y = IIII Chapter ll-- 19. The growth remaining in sitting height, y, at consecutive skeletal age levels is indicated for boys in the graph to the right. Sketch a graph showing the rate of change of growth remaining for the indicated years. Use the graph and your sketch to estimate the remaining growth and the rate of change of remaining growth for a 1S-year-old boy. Determine how to graph the rate of change in the discharge with respect to time. The graph of the rate of change will be positive when the graph of the growth remaining is increasing.t Tn" graph of the rate of change will be negative when the graph of the growth remaining is decreasing. Choose the graph that best represents the rate of change. *8. Determine the remaining growth for a 15-year-old boy. The remaining growth for a 1S-year-old boy is approximately 5. cm. (Round to the nearest integer as needed.) Determine the rate of change of the remaining growth for a '1S-year-old boy. The rate of change is approximately a2 cm less per year. (Type an integer or decimal rounded to one decimal place as needed.) YOU ANSWERED: decreasing.

D.

3.5 3.5 D. c_ A. 1816141a 10Bo 42 ll of l1 - Chapterll- t 9) ft," graph shows the temperature one holiday of an oven. The oven was lit at 8:30 A.M. Let T(x) be the temperature x hours after 8:30 A,M. (a) Find and interpret T'(0.5). How can T'(0.5) be found? A. Find the slope of the line that includes the points (2. * B. Find the slope of the line that includes the points (0. C. Find the change in y-values and add to the change points (0.5,170) and (2.5,850). D. Find the slope of the line that includes the points (5, Find and interpret T'(0,5). Select the conect answer below and fill in the answer box to complete your answer. (Round to the nearest integer as needed.) A. T'(0.5) = ' The oven temperature is T'(0.5)" per hour. e B. T'(0.5) = 340 ; The oven temperature is per hour. c' T'(0.5) = ' The oven temperature is (b) Find and interpret T'(3). Select the correct answer below and fill in the answer box to complete your answer. (Round to the nearest integer as needed.) A. T'(3) = ; The oven temperature is in hour. B. T'(3) = ' The oven temperature is dt hour. vc. t'(3) = Q ;The oven temperature is n< (c) Find T'(6.75)" (Round to the nearest integer as needed.) *A. T'(6.75) = - 340 ; The oven temperature ir lr'1o.zsyl' per hour. B. T'(6.75) = " The oven temperature ir lr'1o.zsyl' per hour. c. T'(6.75) = (d) At a certain time, a turkey was put into the oven, causing the oven temperature to drop. Estimate when the turkey was put into the oven. At which point in the graph is the oven temperature going down? * A. /h.n the slope of the line starts decreasing. B. When the slope of the line starts increasing. C. When the slope of the line is 0. Estimate when the turkey was put into the oven. -D 10:30 11:30 12:30 9 of l1 Chapter I3III) :

;Student:lID :Oate: fal lnstructor:ff Gourse: 2. Find the open intervals where the function graphed below is a) increasing, or b) decreasing. Find the open intervals where the function graphed below is a) increasing, or b) decreasing" Assignment: Chapter 13 a) List any interval(s) on which the function is increasing. Select the correct choice below and fill in any answer boxes within your choice. A. (Type your answer in interval notation. Use a con as needed.) B. The function is never increasing. b) List any interval(s) on which the function is decreasing. Select the conect choice below and fill in any answer boxes within your choice, A. (Type your answer in interval notation. Use a con as needed.) B. The function is never decreasing. a) List the open interval(s) on which the function is increasing. Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. The function is increasing on the interval(s) (Type your ansyyer in interval notation. Use a con as needed. B. The function is never increasing. b) List the open interval(s) on which the function is decreasing. Select the correct choice below and, if necessary fill in the answer box to complete your choice. The function is decreasing on the interval(s) (Type your answer in interval notation. Use a con as needed.) The function is never decreasing, A.

B. I of 8 Chapter I:IID 3. Suppose that the graph below is the graph of f '(x), the derivative of a function f(x). Find the open intervals where f(x) is a) increasing, or b) decreasing. a) List any interval(s) on which the function is increasing. Select the correct choice below and fill in any answer boxes within your choice. A. (Type your answer in interval notation. Use a con as needed.) B. The function is never increasing. b) List any interval(s) on which the function is decreasing. Select the correct choice below and fill in any answer boxes within your choice. A. (Type your answer in interval notation. Use a con as needed.) B. The function is never decreasing. 4. For the following function, find (a) the critical numbers, (b) the open intervals where the function is increasing, and (c) the open intervals where it is decreasing. f(x) = xa + 12x3 +28x2 + 6 (a) ldentify the critical numbers of the function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Tfre critical number(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no critical numbers. (b) ldentify the open intervals where the function is increasing. Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. The function is increasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There are no intervals where the function is increasing. (c) ldentify the open intervals where the function is decreasing. Select the correct choice below and, if necessary fill in the answer box to complete your choice. The function is decreasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) There are no intervals where the function is decreasing" A. 2 of 8 B. fr Chapter l3{I|| 5. For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing. rt*l=#*g a) Find the critical number(s). Select the correct choice below and, if necessary fill in the answer box to complete your choice.

A. The critical number(s) islare (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no critical numbers. b) Determine the interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. List any interval(s) on which the function is increasing. (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing. c) Determine the interval(s) on which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. List any interval(s) on which the function is decreasing. (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never decreasing. 6" Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of liters) is given by the function C(x) = v3 - 3x2 + 6x + 50. a) \Mere is C(x) decreasing? blWhere is C(x) increasing? a) Select the correct choice below and fill in any answer boxes within your choice. A. The function is decreasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function is never decreasing. b) Select the correct choice below and fill in any answer boxes within your choice. A' tne function is increasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function is never increasing. 3 of 8 II- chapter l3ilIl 7 ' The function A(x) = g.gg2x3 - 0.03x2 + 0.14x+ 0.03 approximates the blood alcohol concentration in a person's bloodstream x hours after drinking 8 ounces of a hard liquor. The function only applies to the interval [0,6]. On what time intervals is the blood alcohol concentration increasing? On what intervals is it decreasing? Determine the interval(s), if any, on which the blood alcohol concentration is increasing, Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Tne blood alcohol concentration is increasing on the time interval(s) (Type your answer in interval notation. Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) B. The blood alcohol concentration is never increasing. Determine the interval(s), if any, on which the blood alcohol concentration is decreasing. Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. The blood alcoholconcentration is decreasing on the time interval(s) (Type your answer in interval notation. Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) B. The blood alcohol concentration is never decreasing, 4 of 8 {-I Chapter l3llD 8. The following graph shows the horsepower and torque as a function of the engine speed for a 1964 sports car. a. On what intervals is the power increasing with engine speed?

b. On what intervals is the power decreasing with engine speed?

c. On what intervals is the torque increasing with engine speed?

d. On what intervals is the torque decreasing with engine speed?

a. Determine the interval(s) of engine speed, measured in the engine speed. Choose the correct answer below. A. (2500,4000),(5000,6000) c. (2500,3600) E. (2500,3600),(5000,6000) G. (3600,s000) b. Determine the interval(s) of engine speed, measured in the engine speed. Choose the correct answer below. A. (2500,3600) c. (2500,3600),(4500,6000) E. (2500,3600),(5000,6000) G. (5000,6000) A. (5000,6000) c. (2500,3600),(5000,6000) E. (3600,5000) G. (2500,3600),(4500,6000) A. (2500,3600) c. (3600,s000) E. (5000,6000) G. (2500,3600),(5000,6000) 2.5 3.0 3.5 4.0 4 5 5.0 5 5 6.0 Engine Speed (RPM in '1000s) RPM, over which the power is an increasing function of B. (2500,3600),(5000,6000) D. (2500,s000) F. (5000,6000) H. None RPM, over which the power is a decreasing function of B. (2500,4000),(5000,6000) D. (3600,5000) F. (2500,5000) H. None B. (2500,4000),(5000,6000) D. (2500,5000) F. (2500,3600) H. None B. (2500,3600),(4500,6000) D. (2500,5000) F. (2500,4000),(5000,6000) H. None c. Determine the interval(s) of engine speed, measured in RPM, over which the torque is an increasing function of the engine speed. Choose the correct answer below. d. Determine the interval(s) of engine speed, measured in RPM, over which the torque is a decreasing function of the engine speed. Choose the correct answer below. rccfof!

0))goF oc 0)oo- 2 2 1 1 5 of 8 Chapter t3-II 9. Find the locations and values of all relative extrema for the function with the graph below. mrnrmum maximum Suppose that the graph below is the graph of f '(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. The function has a local (1) atx= Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) A. There is not enough information given. B' fhe function f(x) has a relative maximum al x = no relative minimum. C. The function f(x) has a relative maximum at x = relative minimum at x= D' tne function f(x) has a relative minimum at x = no relative maximum. E. The function f(x) has no relative eldrema. of (1) 10 6 of8 lII:r Chapter l3{ID 11. Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = - x3 * 3x2 +24x+ 4 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. There are no relative maxima. The function has a relative minimum of x= (Use a comma to separate ans\ivers as needed.) B. There are no relative minima. The function has a relative maximum of at x= (Use a comma to separate answers as needed.) G. The function has a relative minimum of of at x= (Use a comma to separate answers as needed.) D. There are no relative extrema. atx= and a relative maximum 12. Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = xa - 32x2 +256 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The function has a relative maximum of atx= and a relative minimum of atx= (Use a comma to separate answers as needed.) B. There are no relative maxima. The function has a relative minimum of x= (Use a comma to separate ansvyers as needed.) G' There are no relative minima. The function has a relative maximum of - (Use a comma to separate answers as needed.) D. There are no relative exlrema. 13. For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per unit that produces maximum profit; and c) the maximum profit, P. C(q)=80+11q; P=71-2q a) The number, q, of units that produces maximum profit is q = b) The price, p, per unit that produces maximum profit is p = E at at 7 of 8 c) The maximum profit is P = $ IIIF Chapter 13|!l 14. Social psychologists have found that as the discrepancy between the views of a speaker and those of an audience increases, the attitude change in the audience also increases to a point but decreases when the discrepancy becomes too large, particularly if the communicator is viewed by the audience as having low credibility. Suppose that the degree of change can be approximated by the function f(x) = - *4 - 4*3 + 36x2, where x is the discrepancy between the views of the speaker and those of the audience, as measured by scores on a questionnaire. Find the amount of discrepancy the speaker should aim for to maximize the attitude change in the audience, The amount of discrepancy to aim for is on the discrepancy scale (Type an integer or decimal rounded to the nearest tenth as needed.) 8 of 8 'ITII