Application of derivatives Questions and Answers

A sphere is to be designed with a radius of 12 cm Use differentials to estimate the maximum error when measuring the surface area of the sphere if the possible error in measuring the radius is 0 25 cm Hint The formula for the surface area of a sphere is A r 4tr O 75 398 cm O 1809 557 cm O 301 593 cm O 452 389 cm

Find the derivative of f x 5x log 2x4 13 O f x 80x4 2x 13 80x4 2x4 13 In7 O f x O f x 10xlog7 2x4 13 O f x 10xlog7 2x4 13 40x5 2x4 13 In7 40x5 2x4 13

Find the derivative of y In O O 313 dx dx dx 1 6x 4 18x 1 6x 4 sinx 2 18x 6x 4 18x 6x3 4 1 sinx 1 cotx cotx 6x 4 sinx

Find the derivative of y 12x4 8cscx O y 48x3 8cscxcotx 5 7x6 y 48x 35 O X O y 48x O y 48x 36 X 35 35 6 x 8cscxcotx 8cscxcotx 5 8cscxcotx X

Find the derivative of f x 2x159x 1 O f x 72x3 59x 1In5 O f x 8x 59x 1 18x4 59x 1n5 O f x 8x 59x 1 18x4 59x 1 O f x 8x 59x 1n5

All the edges of a cube are increasing at a rate of 6 2 centimeters per second How fast is the volume changing when each edge is 10 centimeters long O O O dV dt dV dt dV dt dV dt 300 cm sec 2700 5580 3 1860 cm sec cm sec 3 cm sec

Find the derivative of f x 4x5 11sinx O f x 20x4 11cosx 3350 6 X O f x 20x4 11cosx O f x 20x4 11cosx O f x 20x4 11cosx 35 x6 X 7 5x4 7 4 5x4 7 X 5

Alex Rodriguez hits the baseball at 70 mph at an angle of 30 How far does the ball go and how long does it take to get there

What is the average rate of change of f x from x 3 to x 1 37 Please write your answer rounded to the nearest hundredth f x 3x 3x 6 swer x

For what numbers x 2x x 2 does cscx 1 Refer to the graph which shows y csc x in blue and y sin x in red In the interval 2x x 2x what is the smallest value of x for which csc x 1 the expression Simplify your answer

17 A drug company wishes to test a new drug A researcher assembles a group of volunteers and randomly assigns them to one of two groups one to take the drug and one to take a placebo In addition the company wants the experiment to be double blind What is the meaning of double blind in this situation A The volunteers in both groups are blindfolded when they take the drug or placebo B the volunteers in both groups do not know whether they are taking the drug or the placebo C Neither the volunteers nor the drug company executives know which volunteers are taking the drug and which are taking the placebo D Neither the volunteers nor the evaluator now which volunteers are taking the drug and which are taking the placebo E as long as the subjects are randomly assigned to the two groups there is no need to make the experiment double blind

or what numbers x 2 x 2 does the graph of y tan x have vertical asymptotes Refer to the graph which shows y tan x in blue and y cos x in red In the interval 2 x 2 what is the smallest value of x for which the graph of y tan x has a vertical asymptote A K Type an exact answer using as needed Use integers or fractions for any numbers in the expression Simplify your answer

Two objects start at the same location at noon One object moves due East at a rate of 5 meters per minute The other object moves North Northwest at exactly the same rate so that the angle between them remains fixed at 120 degrees At what rate is the distance between these two objects changing when they have each traveled 50 meters 0 120 Enter an exact answer The law of cosines c a 6 2 a b cos 0 may be helpful

the blank the appropr phrase All items or people of interest in an experiment are collectively called a statistic population cluster

Evaluate lim 1 x5 2x 1 x5 1 Give an exact answer

A box with an open top and a rectangular base is to be constructed from 24 square feet of cardboard The length of the base of the box is twice its width Find the largest possible volume of the box and its dimensions Be sure to give exact answers fractions not decimals Length of long side of base Length of short side of base Height of optimal box

Find two positive numbers and y such that the product of x and y is 45 and the sum of 5 times a and 4 times y is a minimum What is this minimum sum y Minimum sum

Let f x x 4x Then f has two critical numbers One critical number is at x 0 At what x value is the other critical number located Is there a local maximum or a local minimum located at this second critical number O There is a local minimum located at the nonzero critical number O There is a local maximum located at the nonzero critical number f also has two inflection points One is located at x 0 At which z value is the other inflection point located C

5 4 3 2 5 4 NWA 3 2 2 3 4 5 2 3 4 At the point shown on the function above which of the following is tru Of 0 f 0 Of 0 f 0 Of 0 f 0 Of 0 f 0

or the following exercises graph the equations and shade the area of the region between the curves If ecessary break the region into sub regions to determine its entire area 14 y sin 7x y 2x and x 0 15 y 12 x y and y 1 16 y sin x and y cos x over x T

A rectangle with a length of 40 in and a width 25 in has sides that are changing The length is increasing by 4 in per second and the width is decreasing by 3 in per second What is the rate of change of the perimeter Question 10 Select an answer inches per second per second seconds per inch seconds inches 4 pts 1

Fill in the blank with an appropriate word or phrase A subset of a population used by statisticians to make predictions about a population is called a A subset of a population used by statisticians to make predictions about a population is called a cluster sample mean

Stephen makes 14 00 per hour plus 4 1 commission If he works 15 hours and had 2144 worth of sales what were his earnings that we k

on sells doors and is paid 650 per week plus a step commission based on his sales He receives 3 on sales up to the first 1 000 6 on sales between the next 1000 and 2000 nd 15 on remaining sales over 2000 Last week he sold 2600 00 worth of doors How much did he make that week or the toolbar press ALT F10 PC or ALT FN F10 Mac

Store A has put a video game with a regular price of 22 95 on sale at 10 off Store B has the same video game for 20 50 Which store has the better buy

Skis that regularly sell for 329 99 are marked down in price by 25 The next week the store offers a further discount of 15 a What is the final sale price b What is the total discount

retailer buys a set of luggage for 95 50 It is marked up by 48 of his cost Find the profit if it is 40 of the markup

QUESTION 11 A portable speaker sells for 129 95 and the rate of margin is 40 Calculate the cost QUESTION 12 Headsets sell for 119 95 and the rate of margin is 48 Calculate the rate of markup For the toolbar press ALT F10 PC or ALT FN F10 Mac

Find the length of the arc formed by y In cos x from x 0 to x 2 12

The cost of an article is 142 The markup is 41 of the selling price What is the selling price

A wallet sells for 56 It has been marked up by 36 of the cost What is the cost

A small company of science writers found that its rate of profit in thousands of dollars after t years of operation is given by the function below 1 3 P t 7t 7 t 2t 2 a Find the total profit in the first three years b Find the profit in the fourth year of operation c What is happening to the annual profit over the long run a The profit in the first three years is Round to the nearest dollar as needed

The rate at which a substance grows is given by R x 185e0 5x where x is the time in days What is the total accumulated growth during the first 1 5 days Set up the definite integral that determines the accumulated growth during the first 1 5 days 0x 0 Type exact answers in terms of e Growth

5 3 points Find the points of inflection and discuss the concavity of the graph of the function f x 3x 5x

Question 11 of 15 Step 1 of 1 Correct What is the average rate of change of f x from x 2 to x2 6 Please write your answer as an integer or simplified fraction Answer f x 4x 2 Keyp Keyboard Shor

K Approximate the area under the graph of f x and above the x axis with rectangles using the following methods with n 4 f x 8x 6 from x 2 to x 4 a Use left endpoints b Use right endpoints c Average the answers in parts a and b d Use midpoints a The area approximated using the left endpoints is b The area approximated using the right endpoints is c The average of the answers in parts a and b is d The area approximated using the midpoints is

Given the point in polar coordinates find two other polar coordinate representations wit r 0 87 8 8 8 3 2T 3 4T 3 8 8 8 71 3 8 10x 3 2T 3 5T

Write the solution set for the general solution T 4sin x 2 4 2 O O xlx 2nt x 4 xlx T xlx 2nx x 2 xlx 3 T 12 3 2 2nx x 5 12 2nx 7x 2n 12 2n 3 T 2nx x 2n 2 4

Evaluate the following integral 5x x 8 dx 5x x 8 dx Type an exact answer

Next question Find the open intervals where the function f x 4x 24x 165x 7 is concave upward or concave downward Find any inflection points Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function has a point of inflection at Type an ordered pair using integers or fractions Simplify your answer Use a comma to separate answers as needed OB The function does not have an inflection point Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is concave upward on the interval s Type your answer in interval notation Use integers or fractions for any numbers in the expression Simplify your answer Use a comma to separate answers as needed OB The function is never concave upward Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is concave downward on the interval s Type your answer in interval notation Use integers or fractions for any numbers in the expression Simplify your answer Use a comma to separate answers as needed OB The function is never concave downward

Find the locations and values of all relative extrema for the function with the graph below Ay 10 10 8 5AER b 4 ID The function has a local of at x

An airplane climbs at an angle of 11 at an average speed of 420 mph How long will it take for the reach its cruising altitude of 6 5 mi Round to the nearest minute pane 5 min 1 min 4 min 53 min to

A swimming pool as a depth of 4 ft at the shallow end and 8 ft at the deep end The bottom of the pool slopes downward at an angle of 5 7 How long is the pool Round to the nearest foot 53 ft 49 ft 31 ft 40 ft

Re write the equation so the coefficient on x is positive y 5cos 2x 3 y Scos 2x 5 y 5cos 2x 3 3 O y 5cos 2x y 5cos 2x RM 3 3 3 3

Find the exact value sin arcsin 2 3 2 NK N 2

Find a unit vector that is orthogonal to the plane determined by the vectors v 2i 3j k and w 2i 4j 3k

Please show ALL WORK or no credit will be given 1 Find a polar equation for the conic with a focus at the pole and the given eccentricity and directrix Identify the conic and graph it Upload a picture of your grap a e 5 4 x 4 b e 1 y 2

3 Sketch a graph of the equation and upload a picture of the graph Label all intercepts x y 2z 8

Find the derivative of y with respect to x if y e x 33 11

2 Write an equation for the sphere with the given point at its center and the given number as its radius 1 5 8 5