Application of derivatives Questions and Answers

1 1 y y at Final Position m 82 44 102 51 163 46 286 88 461 45 722 53 let y letx T Yotat 17 92x 23 962 Plot a graph for this data and determine the acceleration Time sec 6 7 9 12 15 20 Y 2 o x yo Eq n in y mx b form

A 11 630 g milk chocolate bar is found to contain 7 815 g of sugar Part A How many milligrams of sugar does the milk chocolate bar contain Express your answer in milligrams to four significant figures View Available Hint s 7815 mg Bull Comit Previous Answers Correct The unit analysis method is used in everyday activities This method is very useful in quantifying the terms and making conversions used frequently in the analysis of different substances Part B What will be the amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 11 630 g to 5 000 g Express your answer in milligrams to four significant figures View Available Hint s

ind all vertical asymptotes of the given function 9 16 g x 2 25 A none C x 5 x 5 x 9 B x 5 x 5 D x 5 x

11 Use the slicing method to find the volume of a pyramid with a square base sides of 3 and height of 5 do not use the formula memorized from geometry 3 y

Determine the limit by sketching an appropriate graph 9 x2 0 x 3 3 x 5 X 5 12 lim f x where f x X 5 A 3 3 5 B 0 C Does not exist D

Find the indicated values for the function f x 4x 8 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 2 0 Round to the nearest hundredth as needed OB The function value is not a real number Select the correct choice below and if necessary fill in the answer box to complete your choice O A f 1 B The function value is not a real number Round to the nearest hundredth as needed Select the correct choice below and if necessary fill in the answer box to complete your choice OA f 1 Round to the nearest hundredth as needed B The function value is not a real number

For the given function find f 23 f 60 f 31 and f 129 f x x 4 Find f 23 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 23 3 Simplify your answer OB The root is not a real number Find f 60 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 60 4 Simplify your answer B The root is not a real number Find f 31 Select the correct choice below and if necessary fill in the answer box to complete your choice L OA f 31 Simplify your answer OB The root is not a real number

Find the following root 5 1 32

Find the following Assume that the letter 5 5 5 5

Find the following Assume that variables can represent any real number a 5 a 5

For the given function find f 23 f 60 f 31 and f 129 3 f x x 4 Find f 23 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 23 3 Simplify your answer OB The root is not a real number Find f 60 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 60 OB The root is not a real number Simplify your answer

Find the indicated values for the function f x 4x 8 FFF Select the correct choice below and if necessary fill in the answer box to complete your choice A f 6 OB The function value is not a real number Round to the nearest hundredth as needed

K The number of farms in the United States t years after 1925 is f t million where f t is graphed in Figure A and f t and f t are graphed in Figure B Click the icon to view Figure A Click the icon to view Figure B a Approximately how many farms were there in 1975 million farms Type an integer or decimal rounded to the nearest tenth as needed Figure A 6 5 4 3 2 y 1 0 10 20 y f t 30 40 50 60 70 t X Figure B 0 05 1 Y 10 20 30 40 50 y f t y f t Print b Done 60 Clear all 70 t X Check answ

f 5 4 f x 0 for x 5 f 5 0 and f x 0 for x 5 Choose the correct graph below O A 5 4 Al X Q OB 5 4 O C Ay 5 4 4 D 5 4 X

Which of the functions below are decreasing for all x B A Ay X X D X X Q C O Points 0 of 1 Select the correct choice below and if necessary fill in the answer box to complete your choice A Save Type A B C or D Use a comma to separate answers as needed OB None of the functions are decreasing for all x

Sketch the graph of a function that has the properties described below f 1 3 f 1 0 concave up for all x Choose the correct graph below O A OE 3 1 1 3 X X OB OF 1 3 1 3 X X Q Q Q OU E O C O G 1 0 X 1 0 X Q O D OH Ay 1 3 3 1 X X Q Q

Luna is saving up for a pair of noise cancelling headphones She has some money saved up from her birthday and is also babysitting to earn more money The table gives data about the hours Luna has baby sat and the total money she has saved Hours of baby sitting Total dollar earnings 2 3 5 6 87 98 25 117 Write an equation that gives the total money she has saved S after baby sitting for h hours

Given a differentiable function f x y which of the following are correct statements about the directional derivative Duf at a point xo yo Select all that apply The direction u rapidly at xo yo u is a unit vector 2006 Vf xo yo is the direction in which f increases most Duf xo yo f xo yo u Du f x0 30 is always a positive number The maximum directional derivative of fat ro 40 is f 2o 30 T 0 ra a

Which of the following is impossible A Two parallel lines with the same intercept B Two perpendicular lines with the same y intercept C Two horizontal lines with the same slope D A horizontal line with no x intercept

Line I passes through 7 15 and a b for some values of a and b a Find values for a and b so that line is vertical b Find values for a and b so that line 1 is horizontall 1 Find values for a and b so that line I is perpendicular to y z 2

Roscoe had 3 large 1 topping pizzas delivered to his house and paid a total of 40 72 Calliope had 2 large 1 topping pizzas delivered to her house from the same pizza chain and paid a total of 28 73 What is the delivery fee Ignore sales tax

Let 2 lim f x 3 lim f x I Sketch the graph of this function and find following limits if they exist if not enter DNE 1 lim f x I 19 4 lim f x I 9 5 lim f x I f x 81 C 6 lim f x OF T2 9 if a 9 if 9 x 9 if z 9

Find the x and y coordinates of this function s relative extrema f x x 2 X 4 Relative Minimum at Relative Maximum at Enter

10 A spring has a natural length of 15 in A 900 lb force stretches the spring to 20 inches a b C Find the force constant How much work is done in stretching the spring from 15 in to 18 in How far beyond its natural length will a 2000 lb force stretch the spring

3 For the years 1995to 2002 the number N of cellular phone subscribers in millions can be modeled by the equation N 17 4x 36 1x 83 8 where x 0 represents the year 1995 If this trend continued in what year did the number of subscribers reach or surpass 3750 million

2 A small cube of palladium measures 65 36mm on each side The mass of the cube is 3 36kg Calculate the density of platinum in g cm and report your answer to the correct number of significant figures

9 Consider the following hypothetical data on the occurrence of hepatitis in two cities a Calculate the cumulative incidence of hepatitis in each city b Which city has the higher cumulative incidence City City A City B New cases Observation period 85 90 Total January December 2017 January December 2017 10 The table below displays hypothetical data of 1 year diarrheal disease risks for 1 900 adults working in daycare centers in Georgia Treat their job duties as a way of understanding their exposure Remember risk is another way of saying cumulative incidence Certified childcare providers for children ages 0 3 years exposed Office staff not exposed Disease 50 9 59 No Disease 950 891 Starting population at risk 85 000 150 000 1 841 Total 1000 900 1 900 Risk Re Risk among the exposed Ru Risk among the unexposed a What is the 1 year risk cumulative incidence of disease for the exposed per 1 000 population Hint you will not need a calculator to got

1 point 5 3 is a solution to the system of equations 2a y 7 x y 2 True False

Find the general expression for the slope of a line tangent to the curve of y x 2x at the point P x y Then find the slopes for x 2 and x 0 5 Sk the curve and the tangent lines What is the general expression for the slope of a line tangent to the curve of the function y x 2x at the point P x y mtan The slope for x 2 is The slope for x 0 5 is Sketch the curve of y x 2x and the line tangent to it at x 2 Choose the correct graph below A O B O C Ay tongent to the curve of y x 2x at x 0 5 Choose the correct graph below O D G

Suppose that x and y are related by the equation 3x 4y 2 and use implicit differentiation to determine dy dy

Integrate the given function dx 5 4x dx 5 4x

The displacement s in m of an object is given by the following function of time t in s s t 2t 4t Find the object s acceleration when t 2 When t 2 the acceleration is m s Simplify your answer

The electric current in a microprocessor circuit is 0 370 A How many coulombs pass a given point in the circuit in 2 30 ms

A hoist mechanism raises a crate with an acceleration in m s a 1 0 25t where t is the time in seconds Find the displacement of the crate as function of time if v 0 m s and s 3 m for t 0 s The displacement of the crate is given by s Type an expression using t as the variable

What is the velocity in ft s of a sandbag 2 25 s after it is released from a hot air balloon that is stationary in the ai The velocity is ft s

Find the area bounded by the following curves 3 y x x 2 x 1 y 0 The area is Simplify your answer

59 60 Using right triangles Use a right triangle sketch to complete the following exercises 59 Suppose cos 5 13 Find sin 0 and tan 0

a The graph of y f x is shown Draw the graph of y f x b The graph of y g x is shown Draw the graph of y g x

61 Explain why or why not Determine whether the following state ments are true and give an explanation or counterexample a The range of f x 2x 38 is all real numbers b The relation y x 1 is not a function because y 2 for both x 1 and x 1 c If f x x then f 1 x 1 f x d In general f f x f x e In general f g x g f x f By definition f g x fog x g If f x is an even function then cf ax is an even function where a and c are nonzero real numbers h If f x is an odd function then f x d is an odd function where d is a nonzero real number i If f is both even and odd then f x 0 for all x 62 68 Working with diff

Verify that the indicated function is a solution of the given differential equation 1 2y y 0 y e x 2 2 y 25 y y 5 tan 5x 3 y 2xy y y y c x dP 4 P a bP P dt ac eat 1 bc eat 5 x y dx x xy dy 0 c x y xey x 6 y y y cosha sinh r 7 y 3y 3y y 0 y x e

Find the moment of inertia with respect to the y axis for a flat plate covering the region bounded by y 1 x The moment of inertia is approximately Round to two decimal places as needed 1 6 the x axis x 0 and x

Use integration by parts to evaluate the integral x x 4 dx x x 4 dx

For a voltage V 270 sin 100 t find the root mean square voltage for one period Vrms V

Evaluate the integral S dx 2 25 x dx fx2 0 25 x

Evaluate the integral 14e7x 1dx

A mountain climber is about to haul up a 60 m length of hanging rope How much work will it take if the rope weighs 0 45 N m The amount of work required is Type an integer or a decimal J

A force of 16 N will stretch a rubber band 8 cm 0 08 m Assuming that Hooke s law applies how far will a 4 N force stretch the rubber band How much work does it take to stretch the rubber band this far How far will a 4 N force stretch the rubber band m Simplify your answer

When a particle of mass m is at x 0 it is attracted toward the origin with a force whose k magnitude is If the particle starts from rest at x b and is acted upon by no 2 X other forces find the work done on it by the time it reaches x a 0 a b Set up the integral that gives the work required Use limits of integration in increasing order dx Type exact answers

It takes 1100 J of work to stretch a spring from its natural length of 1 m to a length of 2 m Find the force constant of the spring The spring s force constant is N m Type an integer or a simplified fraction

Evaluate the integral integral 488x 3 dx 0 48e x 3 48 3x 3 dx