Reference: Calculus and Its Applications, 12th, by Marvin L. Bittinger and David Ellenbogen Book

Elementary Applied Calculus

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These are practice questions

Links to Book Below:

1. Calculus And Its Applications, Brief Version 12th edition | Print ISBN - 9780135164884, eText ISBN - 9780135225103 | VitalSource

2. Bittinger, Ellenbogen, Surgent & Kramer, Calculus and Its Applications: Brief Version, 12th Edition | Pearson

These are practice questions

11. Find a) any critical values and b) any relative extrema. f(x) = x -2x+4 a) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The critical value(s) of the function is/are (Use a comma to separate answers as needed.) O B. The function has no critical values. b) Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. The relative maximum point(s) is/are and there are no relative minimum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O B. The relative minimum point(s) is/are and the relative maximum point(S) is/are (Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to separate answers as needed.) O C. The relative minimum point(s) is/are and there are no relative maximum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points. 12. Find a) any critical values and b) any relative extrema. t(x) = x" + 5x +1 a) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The critical value(s) of the function is/are (Use a comma to separate answers as needed.) O B. The function has no critical values. b) Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. The relative minimum point(s) is/are and there are no relative maximum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O B. The relative minimum point(s) is/are and the relative maximum point(s) is/are (Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to separate answers as needed.) O C. The relative maximum point(s) is/are and there are no relative minimum points. Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points.13. The graph of a derivative f is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f. Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O A. The function f is decreasing on and increasing on O B. The function f is decreasing on and never increasing- O C. The function f is increasing on and never decreasing. What is/are the x-value(s) of the relative minimum/minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The relative minimum/minima occur(s) at x = (Simplify your answer. Use a comma to separate answers as needed.) O B. There are no relative minima. What is/are the x-value(s) of the relative maximum/maxima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The relative maximum/maxima occur(s) at x = (Simplify your answer. Use a comma to separate answers as needed.) O B. There are no relative maxima. Sketch a possible graph of f. Choose the correct graph below. OA O B. O C. OD14. The graph of a derivative f' is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f. Q Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O A. The function f is increasing on and decreasing on O B. The function f is increasing on and never decreasing- O C. The function f is decreasing on and never increasing What is/are the x-value(s) of the relative maximum/maxima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The relative maximum/maxima occur(s) at x = Simplify your answer. Use a comma to separate answers as needed.) O B. There are no relative maxima. What is/are the x-value(s) of the relative minimum/minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The relative minimum/minima occur(s) at x = (Simplify your answer. Use a comma to separate answers as needed.) O B. There are no relative minima Sketch a possible graph of f. Choose the correct graph below. O A. O B. O C. D. Q Q Q Q Q 15. Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is increasing and over which it is decreasing. Then sketch a graph of the function. f(x) = - 10+5x - x2 Describe any relative extrema. Select the correct choice below and, if necessary, fill in the answer box(es) to within your choice. A. The relative minimum point(s) is/are and the relative maximum point(s) is/are (Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to separate answers as needed.) O B. The relative minimum point(s) is/are and there are no relative maximum points. Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) C. The relative maximum point(s) is/are and there are no relative minimum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points Identify any intervals over which the function is increasing or decreasing. Select the correct choice below and fill in the answer box(es) within your choice. A. The function f(x) is increasing over the interval(s) and is not decreasing anywhere. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The function f(x) is decreasing over the interval(s) and is not increasing anywhere. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) C. The function f(x) is increasing over the interval(s) and decreasing over the interval(s) Type your answers in interval notation. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed.) Choose the correct graph below. O A. O B. O C. OD. Q Q Q Q Q Q16. Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is increasing and over which it is decreasing. Then sketch a graph of the function. G(x)= -x3 +x" +x-6 Describe any relative extrema. Select the correct choice below and, if necessary, fill in the answer box(es) to within your choice. O A. The relative minimum point(s) is/are and the relative maximum point(s) is/are (Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to separate answers as needed.) B. The relative minimum point(s) is/are and there are no relative maximum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O C. The relative maximum point(s) is/are and there are no relative minimum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points. Identify any intervals over which the function is increasing or decreasing. Select the correct choice below and fill in the answer box(es) within your choice. O A. The function G(x) is decreasing over the interval(s) and is not increasing anywhere. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The function G(x) is increasing over the interval(s) and decreasing over the interval(s) Type your answers in interval notation. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed.) O C. The function G(x) is increasing over the interval(s) and is not decreasing anywhere. Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Choose the correct graph below. O A. O B. O c. Q 17. Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is increasing and over which it is decreasing. Then sketch a graph of the function. F(x) = -4+ 5x Describe any relative extrema. Select the correct choice below and, if necessary, fill in the answer box(es) to within your choice. A. The relative minimum point(s) is/are and there are no relative maximum points. (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) . The relative maximum point(s) is/are and there are no relative minimum points. Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O C. The relative minimum point(s) is/are and the relative maximum point(s) is/are (Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points. Identify any intervals over which the function is increasing or decreasing. Select the correct choice below and fill in the answer box(es) within your choice. O A. The function F(x) is increasing over the interval(s) and decreasing over the interval(s) (Type your answers in interval notation. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed.) O B. The function F(x) is increasing over the interval(s) and is not decreasing anywhere. Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O C. The function F(x) is decreasing over the interval(s) and is not increasing anywhere. Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Choose the correct graph below. O A. O B. O C. O D Q Q Q Q18. Find the relative extreme points of the function, if they exist. Then sketch a graph of the function. F(x) = Vx-2 Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The relative maximum point(s) is/are Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no relative maximum points. Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative minimum point(s) is/are (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) B. There are no relative minimum points. Choose the correct graph below. OA O B. O c. O D. Q 19. Find the relative extreme points of the function, if they exist. Then sketch a graph of the function. - 12 G(xX) = = x-+4 Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The relative minimum point(s) is/are Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no relative minimum points. Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative maximum point(s) is/are (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) B. There are no relative maximum points Choose the correct graph below. O A. O B. O c. OD. Q IIIIII LA22. The temperature of a person during a certain illness is given by the following equation, where T is the temperature ("F) at time t, in days. Find the relative extreme points and sketch a graph of the function. T(t) = - 0.2t + 1.6t + 98.6, Osts 8 What are the relative extreme points? Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer. Type an ordered pair. Use integers or decimals for any numbers in the expression. Use a comma to separate answers as needed.) O A. The relative minimum point(s) is/are O B. The relative maximum point(s) is/are C. The relative minimum point(s) is/are and the relative maximum point(s) is/are Sketch a graph of the function. Choose the correct graph below. OA. OB. O C. 110- AT(1) 110- Q 110- a 110- 90- 90- 23. The data in the following table give a measure of nutrition and the projected life expectancy for various countries. Use the data to answer the following questions. Country Measure of Life Expectancy at Birth (in Country Measure of Nutrition Life Expectancy at Birth (in Nutrition years) years) Country 1 1002 76 Country 6 1170 7B Country 2 1012 80 Country 7 603 59 Country 3 716 68 Country 8 1095 76 Country 4 1184 82 Country 9 1274 79 Country 5 760 74 Country 10 B12 75 a) Use regression to fit a cubic function y = f(x) to the data in the table, where x is the measure of nutrition and y is life expectancy. Then fit a quartic function and decide which fits best. Choose the correct answer below. O A. Quartic function O B. Both functions fit well O C. Cubic function b) What is the domain of the function? Type your answer in interval notation.) c) Does the function have any relative extrema? O A. The function definitely has a relative minimum near x = 1100. O B. The function may have a relative maximum near x = 1100. O C. The function definitely has a relative maximum near x = 1100. O D. The function may have a relative minimum near x = 1100. O E. The function has no relative extreme.24. Graph the function. Then estimate any relative extrema. f(x) = - 2x" - 4x" + 10x#+ 12x - 6x7- 8x + 5,000 Graph the function. Choose the correct graph below. O A. OB O c. a Q Q Q Q X = [- 10,10] X = [-10,10] X = [- 10,10] X = [- 10,10] Y = [- 5100, - 4940] Y = [0,6000] Y = [4940,5100] Y = [-10000,1000D] Estimate any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) B. There are no relative maxima. Estimate any relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no relative minima. 25. Use your calculator's absolute value feature to graph the following function and determine the relative extrema and intervals over which the function is increasing or decreasing. State any x-values at which the derivative does not exist 1(x ) = -*2 -8 Choose the correct graph below. Each graph is contained in a window [ - 10,10,1]. O A. O B. OC. OD. Q Q Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The relative minimum point(s) is/are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) B. There are no relative minimum points. Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The relative maximum point(s) is/are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no relative maximum points. Determine where the function is increasing or decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. The function is decreasing on and the function is increasing on (Simplify your answers. Type your answers using interval notation. Use a comma to separate answers as needed.) O B. The function is decreasing on The function is never increasing (Simplify your answer. Type your answer using interval notation. Use a comma to separate answers as needed.) O C. The function is increasing on . The function is never decreasing Simplify your answer. Type your answer using interval notation. Use a comma to separate answers as needed.) D. The function is never increasing nor decreasing Where does the derivative not exist? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The derivative of the function does not exist for x = (Simplify your answer. Use a comma to separate answers as needed.) O B. There are no x-values for which the derivative of the function does not exist