Application of derivatives Questions and Answers

Find the domain and range of the relation 9 5 9 4 9 3 9 2 Then determine whether the relation is a function Domain Range Is the relation a function Yes SO No

4 3 s sqrt 14 1 2 s sqrt 14 least one of the answers above is NOT correct 1 point Starting from the point 5 4 1 reparametrize the curve t 5 1t 4 3t 1 2t in terms of arclength t s 5 5 sqrt14 4 3s sqrt14 1 2s sqrt14 4 1 14 3s 14 2s 14

Match the parametric equations with the graphs labeled A F As always you may click on the thumbnail image to produce a larger image in a new window sometimes exactly on top of the old one A 1 x cos 4t y t z sin 4t 2 x cost y sint z ln t 3 x 1 2 y t z 1 4 x 5 x 1 y 1 1 f z 6 x cost y sin t z sin 5t sin 3t cost y sin 3t sin t z t JU A L FX

We can use sigma notation to rewrite the sum 3 5 7 9 31 as N 3 5 7 9 31 f k k 1 by setting N I and f k

8 As f 0 1 n 1 0 c c 0 f x b tan 2 f x f x 1 Also f x is increasing Vb e R Let a and b be positive real numbers such that a 1 and b a Let P be a point in the first quadrant that lies 1 Suppose the tangent to the hyperbola at P passes through the point 1 0 on the hyperbola x y a b and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes Let A denot the area of the triangle formed by the tangent at P the normal at P and the x axis If e denotes the eccentricity of the hyperbola then which of the following statements is are TRUE B 2 e 2 D A b4 A 1 e 2 C A a A D As in first quadrant if normal at P is making equal intercepts on ares then slope of the normal 1

Assume that females have pulse rates that are normally distributed with a mean of 73 0 beats per minute and a standard deviation of o 12 5 beats per minute Complete parts a through c below a If 1 adult female is randomly selected find the probability that her pulse rate is less than 77 beats per minute The probability is 0 6255 Round to four decimal places as needed b If 16 adult females are randomly selected find the probability that they have pulse rates with a mean less than 77 beats per minute The probability is Round to four decimal places as needed

5 Find the indicated IQ score The graph to the right depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard deviation of 15 Click to view page 1 of the table Click to view page 2 of the table The indicated IQ score x is Round to one decimal place as needed 0 6 X

A 35 foot ladder is set against the side of a house so that it reaches up 28 feet If Bentley grabs the ladder at its base and pulls it 4 feet farther from the house how far up the side of the house will the ladder reach now The answer is not 24 ft Round to the nearest tenth of a foot

Use the remainder theorem to find P 3 for P x x 2x 6x 8 Specifically give the quotient and the remainder for the associated division and the value of P 3 Quotient Remainder P 3 0 0 0 DO X

Find a cubic polynomial that is f x ax bx cx d that has horizontal tangents at the points 5 5 and 4 2 f x 14x 3 135 189x 2 135 2940x 135 Verify your result by plotting the graph of f x

Graph the exponential function g x To do this plot two points on the graph of the function and also draw the asymptote Then click on the graph a function button Additionally give the domain and range of the function using interval notation X I Domain Range 0 0 0 0 0 0 0 0 8 X 8 QUO

The graph below shows the total distance s in miles traveled by a bicyclist after t hours 40mi distance 35mi 30mi 25mi 20mi 15mi 10mi 5mi Omi Ohr 0 5hr 1hr a Estimate the bicyclist s average velocity over the following time intervals Over 0 1 the average velocity is approximately mi hr Over 1 2 5 the average velocity is approximately Over 2 5 3 5 the average velocity is approximately b Estimate the bicyclist s instantaneous velocity at the following times At t 1 2 hour the instantaneous velocity is approximately At t 2 hours the instantaneous velocity is approximately At t 3 hours the instantaneous velocity is approximately mi hr mi hr 1 5hr mi hr mi hr mi hr c Estimate the bicyclist s maximum velocity and the specific time at which it occurs The maximum velocity is approximately mi hr which occurs when t 2hr 2 5hr 3hr hr 3 5hr time 4hr

Fill in the missing values to make the equations true a log 11 log 5 log 5 log b log 11 log log c 3 log 3 log 11 S B X

Let P and P be the populations in hundreds of Town 1 and Town 2 respectively The table below shows data for these two populations for five different years Year 1980 1982 1984 1988 1992 P 41 51 61 71 81 P2 93 86 79 72 65 Find the average rate of change of each population over each of the time intervals below a From 1980 to 1984 the average rate of change of the population of Town 1 was Change of the population of Town 2 was b From 1984 to 1992 the average rate of change of the population of Town 1 was Change of the population of Town 2 was c From 1980 to 1992 the average rate of change of the population of Town 1 was change of the population of Town 2 was hundred people per year hundred people per year hundred people per year hundred people per year and the average rate of hundred people per year and the average rate of hundred people per year and the average rate of

Find an equation of the tangent line to the curve y 7 at the point 1 7 Tangent line y Check your result by plotting the curve and the tangent line together

2 Find a cubic polynomial that is f x ax bx cx d that has horizontal tangents at the points 5 5 and 4 2 f x Verify your result by plotting the graph of f x

The graph below shows the distance traveled D in miles as a function of time t in hours ilm b Based on your results from a what is the rate of change of D AD At 179 97 5 OB It represents the car s velocity C It is the total distance the car travels in five hours OD It is the slope of the line 14 12 5 145 0 5 70 R A 17 5 a For each of the intervals find the values of AD and At between the indicated start and end times Enter your answers in their respective columns in the table At Click on the graph to get a larger version Time Interval t 1 5 tot 4 t 1 tot 2 5 t 0 5 to t 3 5 tr AD c Which of the statements below describes of your response to part b Select all that apply A It is the acceleration of the car over the five hour time interval

Given a power function of the form u s as with u 1 24 and u 3 648 find n and a n

Let p x 2 sin z An equation of the line tangent to the graph of p x at the point 6 1 can be written in the form y mx b where and b m Check your result by plotting the curve and the tangent line together

Answer the questions regarding the graph of f Then use this information to graph the function a Choose the end behavior of the graph of f Falls to the left and rises to the right b List each real zero of faccording to the behavior of the graph at the X axis near that zero If there is more than one answer separate them with commas If there is no answer click on None Zero s where the graph crosses the X axis 0 Zero s where the graph touches but does not cross the X axis c Find the y intercept of the graph of f d Graph f x x x 1 x 1 by doing the following Plot all points where the graph of fintersects the X axis or y axis For each point on the X axis select the correct behavior Click on the graph icon 0 0 X

11 Will this model result in a reasonable answer when t 180 Explain why or why not vill Shan

A monk crossbred plants which can have purple or white flowers and obtained 655 plants with white flowers and 334 plants with purple flowers Find the empirical probability that a plant had each type of flower M The probability a plant had white flowers is Round to the nearest hundredth as needed The probability a plant had purple flowers is Round to the nearest hundredth as needed

Brenda cuts her grass every 8 days and trims her shrubs every 36 days If Brenda cut her grass and trimmed her shrubs on June 1 how many days will it be before she cuts her grass and trims her shrubs on the same day again It will be days before Brenda cuts her grass and trims her shrubs on the same day again

65 and 50 a Find the greatest common divisor GCD b Find the least common multiple LCM a The GCD is Simplify your answer Type an int

Part II Workout Show all the necessary steps for full credit 4 A particle is moving along the graph ofy x graphed in the figure below When x 8 the y component of the position of the particle is increasing at the rate of 2 centimeter per second How fast the x component is changing at this moment How fast is the angle of inclination changing at this moment ii 2 4 0 e 6 8 2 8 10 4 pts

Part ll Workout Show all the necessary steps for full credit 15 pts 4 A particle is moving along the graph ofy x graphed in the figure below When x 8 the y component of the position of the particle is increasing at the rate of 2 centimeter per second How fast the x component is changing at this moment How fast is the angle of inclination changing at this moment i ii 4 pts

The odds against rolling a number less than 2 are Type whole numbers Simplify your answers

t a homeowners association meeting a board member ote yes vote no or abstain on a motion There are three motions hich each board member must vote Complete parts a through elow Determine the number of points in the sample space

A six sided die is tossed Determine the odds aga The odds are Simplify your answer

A box contains three cards On one card there is a rectangle R on another card there is a question mark Q and on the third card there is a moon M Two cards are to be selected at random with replacement Complete parts a through e below T A RR RQ RM MR MQ MM B RQ QM MR C RR RQ RM QR QQ QM MR MQ MM OD RQ RM QR QM MR MQ c Determine the probability that two question marks are selected The probability is 1 9 Simplify your answer d Determine the probability that a card containing a question mark and then a card containing a rectangle are selected The probability is Simplify your answer

is pro s workout schedule is to have both morning and afternoon practice for 3 days rest for 1 day hrave only morning practice for 2 days rest for 2 days and then start the cycle again If the tennis pro is on her r one day part of the schedule determine what she will be doing a 25 days from today b 58 days from today c 110 days from today and d Will the tennis pro have a day off 86 days from today at day of the workout schedule will the tennis pro be on 25 days from now First training day of the cycle Fourth training day of the cycle Third training day of the cycle Second training day of the cycle hat day of the workout schedule will the tennis pro be on 58 days from now Third training day of the cycle 3 Fifth training day of the cycle C Second training day of the cycle O Fourth training day of the cycle the workout schedule will the tennis pro be on 110 days from now Nex

6 0 1 Points DETAILS A PREVIOUS ANSWERS SALGTRIG4 7 4 039 1 11 2 03 In Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION tan 0 4 2 cos 0 1 0 2 2 n 47 MY NOTES 2Tn ASK YOUR TEACHER

2 10 pts 2 pts each Use the function F x graphed below to evaluate the following If a value does not exist write DNE mox on sulu DJELDIENS 39TTICHISI AM ASOS dinsdad a lim F x x 1 c lim F x x 1 e lim F x x 1 TOWER TUC 1 1 no bowolls ton 51521lolesta 99106 diw viernes of equiel maxs b lim F x x 2 d lim F x Priterial anx 1 n 20 1 01

14 6 pts The figure below shows the graph of the derivative f x X4 Arx mix5 mixiggs 302 mod Sulevaisupalotion indW At which of the points 0 X X2 X3 x4 and X5 a 2 pts does the function f has critical points b 2 pts does the function f has local maximums c 2 pts does the function f has inflection point s onil se aq 8 SI x H

dy 6 pts Given x y 4xy Use implicit differentiation to find dx in terms of x and y

Consider the given equation cot y csc y sin y sec y a Verify algebraically that the equation is an identity cos 2 y sec y 1 sin 2 y sin y cosec y sin y This answer has not been graded yet b Confirm graphically that the equation is an identity Hey

Solve by using the square root propery of equality 2 25 0 X Simplify your answer Use a comma to sep answers as needed Type your answer in a bi Type an exact answer using radic as needed

x2 225 X Simplify your answer Use a comma to separate answers as needed Type an exact answer using radicals as needed

2 For an unknown function g x we have the following derivative g x 5x3 20x a Find the critical points of g x b Create a well labeled number line for the first derivative test Clearly label whether each critical point from a is a local max local min or neither c Find the second derivative of g x and then explain how to use the second derivative test to determine whether 0 is a local maximum or a local minimum Write a sentence or two d Find the inflection points of g x Provide exact answers not decimal approximations e Using the evidence from above sketch a possible graph for g x Label your critical points and inflection points

I Let F x 3 t t 40 a Find the value of a where F obtains its maximum value x dt for x b Find the intervals over which F is only increasing or decreasing Use interval notation using U for union and enter none if no interval Intervals where F is increasing Intervals where F is decreasing c Find open intervals over which F is only concave up or concave down Use interval notation using U for union and enter none if no interval Intervals where F is concave up Intervals where F is concave down

Decide whether the statement is true or false If it is false explain why The union of the solution sets of 2x 6 24 2x 6 24 and 2x 6 24 is Choose the correct answer below A False because the union is 9 OB True OC False because the union is 9 U 9 00 OD False because the union is 0 00

Two sets are specified by graphs Graph their union 10 4 10 OB 9 OC 9 Choose the correct union OA 10 4 8 10 8 9 LO 9 7 7 8 8 6 6 7 7 5 5 co 6 6 6 4 5 4 5 5 4 4 3 3 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 1 1 1 2 2 2 2 2 3 3 3 3 3 4 Est 4 4 4 4 5 10 5 5 5 5 6 6 to 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9

Decide what number must be added to make the expression a perfect square trinomial Then factor the x2 0 4x What number must be added to make the expression a perfect square trinomial x 0 4x Type an integer or a decimal

Consider the mathematical system indicated by the table Assume that the associative property holds for the operation a What are the elements of the set in this mathematical system b What is the binary operation c Is the system closed d Is there an identity element for the system under the given operation e Does every element in the system have an inverse f Give an example to illustrate the associative property g Is the system commutative h Is the mathematical system a commutative group A OA yxz y X y NAX XXX N Z y W W W y Z y XN W W X Z W y The elements are Use a comma to separate answe as needed b What is the binary operation Choose the correct answ

Translate the word phrase to an algebraic expression the sum of x and 14 braic expression is

Find the LCM of this set of numbers 10 20 and 50 The

The factors of 200 are Use a comma to separate answers as needed Type each factor only once

Indicate whether 45 Is Is 45 prime or composite O Composite O Prime

Use a calculator to approximate the square root 6 6 Round to three decimal places

The last 36 boat rentals at a boat rental company were 14 sunfish 4 kayaks and 18 rowbo complete parts a through c a Determine the empirical probability that the next boat rental is a sunfish b Determine the empirical probability that the next boat rental is a kayak c Determine the empirical probability that the next boat rental is a rowboat a P sunfish Type an integer or a simplified fraction