Application of derivatives Questions and Answers

If f x 3x 4x 6 find the instantaneous rate of change of f x at x 0 Answer

The following table shows the daily receipts in millions of dollars of the movie Avatar fo successive Fridays after its opening on Friday 18 December 2009 Weeks Receipts 77 025 68 49 42 785 31 28 23 611 13 655 6 526 2 047 0 844 0 92 0 425 0 188 0 076 0 045 0 028 0 2 4 6 8 10 12 14 16 222222 18 20 24 26 28 Estimate the instantan

3 22 54 3 2 1 2 3 hy 2 3 4 5 At the point shown on the function above which of the following is true Of 0 f 0 Of 0 f 0 f 0 f 0 Of 0 f 0 f 0 f 0 f 0 f 0

3 2 1 3 f 0 1 6 2 41 7 2 34 1 2 3 Use the graph of f x above to estimate the value of f 0 to one decimal pla X

Find the rate of change of total revenue cost and profit with respect to time Assume that R x and C x are in dollars R x 60x 0 5x C x 4x 5 when x 30 and dx dt 25 units per day The rate of change of total revenue is per day

You have three identical bags of marbles each one containing 3 marbles one blue one red and one yellow 4 marks a Draw a tree diagram on a separate piece of paper to illustrate all possible outcomes when one marble is drawn out of each bag b What is the probability of all three marbles being the same colour

Question 1 15 marks Consider the functions fi t and f in Fig 1 use the graphical method to compute he convolution f t f t f t 0 14 1 Figure 1 Functions fi t and f t

One card is drawn at random from a pack of 52 cards What is the probability that the card drawn is a face card Jack Queen King or Ace 1 mark

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 1 mark

4 Which of these numbers cannot be a probability 0 0005 a b C d 0 5 1 004 1 30

Use implicit differentiation on y 3 tangent line at the point a dy dx H 4 3 500130 dy 6xy to find and find the equation of the da b The tangent line is y State m and b accurate to at least 4 decimal places

Chubbs Inc s manufacturing overhead budget for the first quarter of 2020 contained the following data Variable Costs Indirect materials Indirect labor Utilities Maintenance Fixed Costs 11 600 Supervisory salaries 11 000 Depreciation 7 000 Property taxes and insurance 5 600 Maintenance 36 800 7 000 7 200 4 700 Actual variable costs were indirect materials 14 500 indirect labor 9 200 utilities 9 600 and maintenance 4 900 Actual fixed costs equaled budgeted costs except for property taxes and insurance which were 8 600 The actual activity level equaled the budgeted level All costs are considered controllable by the production department manager except for depreciation and property taxes and insurance a Prepare a manufacturing overhead flexible budget report for the first quarter List variable costs before fixed costs Budget CHUBBS INC Manufacturing Overhead Flexible Budget Report For the Quarter Ended March 31 2020

n Evaluate as f where f x n 0x 314 01 01 10 4 01 1 20 1 3 1

1 2 3 h x Graph the function Plot all necessary asymptote 2x 4 x 5 10 4 App

St C App ALE FX 1 My www awu aleks com alekscgi x lsl exe 1o u lgNslkr7j8P Homework Question 5 2 The graph of f x

Homework C2S5 Question 4 of 10 1 2 Determine the vertical as

10 Question 1 Let f x 2x 5 O G 5

Question 2 f x 3x 4 5 fin 5x 4 3

Question 3 Let g x 3x 1 Find equation for th

Question 4 Let f x x 1 x x 6 at what point does f x cr

Solve the equation belo 3x x 5 7 x 6 The solution is x 2 x

Can someone please take the inverse Laplace transform of the following function 3 C V s 4 3 x 10 5 6 x 10 0s 4 x 105s 38 to 1015 1010 105 2 3

tx 2 and x 1 ymptote at y 4 r Message instructor

Use logarithms to evaluate each of the following Show all your work 3 91 2 4 8 0 073

Write each expression as a single logarithm log x2 3x 2 2log x 1 13

uct one period of the graph of y cos 2x 2 sin x by the method of addition of ordinates

Find the exact value of each logarithm without a calculator

OF Question 9 4 1 41 PS Part 4 of 4 HW Score 86 03 24 95 of 29 points Points 0 75 of 1 e amount of plutonium remaining from 1 kilogram after x years is given by the function W x 2 How much will be left after 4000 years How much will be left after 9000 years How much will be left after 15 000 years Estimate how long it will take for the 1 kilogram to decay to half its original weight The amount of plutonium left after 4000 years is about 89 kilograms ound the final answer to two decimal places as needed Round all intermediate values to six decim needed The amount of plutonium left after 9000 years is about 77 kilograms und the final answer to two decimal places as needed Round all intermediate values to six decimal places as need The amount of plutonium left after 15 000 years is about 65 kilograms ound the final answer to two decimal places as needed Round all intermediate values to six decimal places as need The time it will take for the 1 kilogram to decay to half its original weight is years

Part 1 of 2 O Points 0 of 1 gross domestic product GDP in trions of dollars for Country A and Country B can be approximated as follows w responds to the year 1960 antry Af x 0 00013 1 103 antry B g x 0 0189 1 868 e trend continues what is the first full year in which the Country As GOP surpasses 37 trilion ich of the following describes how to find the first full year in which Country A s GDP surpasses 37 trillion using the ormation select the correct choice below and fill in the answer box to complete your choice e an integer or a decimal A To find the first full year in which Country A s GDP surpasses 37 trillion find the intersection p graphs y 0 00013 1 103 and y The first full year in which Country A s GDP surpasses represented by the x coordinate B To find the first full year in which Country A s GDP surpasses 37 trillion substitute find f x for x a

gross domestic product GDP in trillions of dollars for Country A and Country B can be approxim rex 60 corresponds to the year 1960 untry A f x 0 00011 1 105 untry B g x 0 0142 1 514 d the projected GDP in 2013 and 2027 for Country A ich of the following describes how to find the projected GDP in 2013 using the given information rect choice below and fill in the answer box to complete your choice pe an integer or a decimal A To find the projected GDP in 2013 find the intersection point of the graphs y 0 00011 1 105 The projected GDP in 2013 is represented by the y coordinate B To find the projected GDP in 2013 substitute for x and evaluate to find f x

The mean age of the parents guardians of a group of third graders is 35 with a standard deviation of 4 Use the 68 95 99 7 normal distribution rule to predict the percentage of the parents guardians over 31 68 84 16 68 95 2018 Gyntyon Inc TR 99 7 30 20 0 0 20 30 Standard deviations

8 f x 6 5 4 3 1 1 2 3 4 2 3 4 The curve above is the graph of a sinusoidal function It goes through the points 4 4 and 2 4 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits 4

signmen vious Problem P bint et v2 2 5

For each of the following curves use implicit differentiation to find and determine the equation of the tangent line at the given point a x y 6xy at 3 3 dy da dy dx 3 3 Equation of tangent line at 3 3 b sin y y x x at 0 0 dy da dy da 0 0 Equation of tangent line at 0 0 c 3xe y y at 0 619061 1 dy dx dy dx 0 619061 1 Equation of tangent lin OC dy dx Round to five decimals

A Honda Civic LX costs 17 000 and is depreciating at a rate of 13 per year A Write a function V t that models the value of the car over time B According to the model what will the car be worth after 8 years C According to the model when will the car be worth 2000

Sue invests 10 000 and wants to long how long it will take her money to grow to 100 000 She invests it at 9 interest compounded monthly How many years will it take for this to happen Work

questions ASULIR GIPUIC aut you a Note You may repeat this tutorial as mar A Three kids Alberto Bernadette and Car split the cookies up provided that none

od 1 5 points Graph the function below at least 3 4 points accurately cogmossb noilsit leineq ad f x 3x Answer the following about the function If there is none write the word none Domain Range X intercept s

7 Let x be the length and width of a rectangular box with a fixed height h 3 A find total surface area S including the top and the bottom in terms of x and the volume V in terms of x Solve x in terms of S then find the formula V in terms of B find dV in terms of dS approximate the increase in volume using dV when S changes from S 320 m to S 321 m 8 Given that x x t y y t are functions oft and that xy y x y Take derivative or d dt on both sides then solve dy dt in terms of x y and dx dt Find dy dt if x 1 y 1 and dx dt 2

x 1 x 10x 25 3 Find the partial fraction decomposition of Show work Make sure you don t just write the values of A B make sure you write what rational expression is equal to in the box below 4 points

K y sin x y sec x y csc x y cos x y tan x y cot x HU 1 6 5 4 3 2 1 1 3 4 5 6

9 A ladder 20 ft long rests against a house If the lower end of the ladder slips along the ground at the rate of 5 ft s away from the house how fast is the upper end of the ladder coming down when it is 15 ft above the ground 10 We want to fence in a rectangle and divide it into three parts with two fences parallel to one of its side Find the largest such rectangle may be fenced off with 300 yards of fences C w

Use synthetic division and remainder theroem f x 3x 3 8x 2 3x 2

daily a Which CD earns more interest b By how much 15 ALGEBRA Kati Sweigart invests 100 000 in a 4 year CD at 6 75 compounded monthly a Find amount and interest using tables b Find amount and interest using the formula ALGERDA T 65 000 C

8 Elliot Chambers invests 30 000 in a 1 year CD that earns interest at an annual rate of 3 75 compounded monthly a What is the amount of the CD at maturity b What is the interest earned 9 Emily Gast deposits 50 000 in a 4 year CD that earns interest at an annual rate of 5 25 compounded daily a Find the amount of the CD in 4 years b Find the interest earned in 4 years

The function f x y 3x 3y has an absolute maximum value and absolute minimum value subject to the constraint 4x 4xy 4y 4 Use Lagrange multipliers to find these values The absolute maximum value is Type an exact answor

3 This circle graph pie chart represents how Harriet spent 500 000 Examine this graph and then answer the questions on the ne Gifts 10 Unused 30 New H

Use Lagrange multipliers to find the point on the surface 3x y 5 0 closest to the point 1 6 3 HIEKH The point on the surface 3x y 5 0 closest to the point 1 6 3 is 0 Type exact answers

Find the minimum and maximum distances between the sphere x y z 9 and the point 5 6 9 The minimum distance is Type an exact answer using radicals as needed

Find sin2x cos2x and tan2x given cosx and sinx C