Application of derivatives Questions and Answers

Match each of the following graphs with the expect function by placing the letter of the graper on the line provided Ench letter can only be used unce Do not use a calculator os desnue to draw the graph H 1700 1 1 E 1 x x 1 4 C0 70x x Qwi 5 700 1 2 1 q 1 x 1 x 1 B a 9 1 bia Cro 51 CAD 0 2 27 CNB Cz 7 x x 2x 2 QUI cia XI X 2 1 F D 12 10 1 0 Dat 14 1 1 0 72 x 11 0 26 2 1 1 B38 x x 2x o x 1 2 1 1 1 1 9 f x x 2x 21 10 11 16 x f 1 1 2 1 1 1 0 D 10 f x x x 2 y 1 x 1 0 1 1 X 1 0 1 1 1 4 1 0 Y 1 1 4

A central angle measuring 165 is in a circle of radius 4 meters Find the length of the arc of the circle subtended by the angle Make the figure before solving the problem X Correct Answer about 660 meters about 11 5 meters about 2 9 meters about 4 meters about 11 5 meters about 4 meters

Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the graph H 3 f x x 1 E 4 f x x 1 B 5 f x x 2x 1 q 1 x Q 1 b 1 C O G 6 f x x 2x 1 x 1 x 1 7 f x x 2x 2 a 1 6 2 x 2 a 3 1 1 1 2 1 2 0 8 f x x 2x o b a 2 a D 9 f x x 2x x 1 x 1 0 2 2a 2 a 1 f 1 1 1 2 1 1 1 1 27 1 0 x 2 2 x 12 10 f x x 2x 2 x 1 x 2 2 1 1 2 1 3 1 1 2 21 1 0 f 1 2 1 12 1 12 0 2 0 1 1 1

Definition The collection of all antiderivatives of f is called the indefinite integral of f with respect to x and is denoted f x da Find the most general antiderivative by evaluating the following indefinite integral 5 x 12 0 dz NOTE The general antiderivative should contain an arbitron

A street light is at the top of a 12 ft tall pole A woman 6 ft tall walks away from the pole with a speed of 7 ft sec along a straight path How fast is the tip of her shadow moving when she is 50 ft from the base of the pole ft sec

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute It forms a pile in the shape of a right circular cone whose base diameter and height are always equal How fast is the height of the pile increasing when the pile is 22 feet high Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 V r h 3 ft min

Next question Get a similar question You can retry this question below Given P x x 2x 25x 50 find the zeros real and non real of P The zeros are 2 51 5i Write P in factored form as a product of linear factors Be sure to write the full equation including P x 0 2 0 5i 0 5i syntax error this is not an equation

The volume of a cylinder of height 12 inches and radius r inches is given by the formula V 12m dV Which is the correct expression for O O dV dt dV dt dV dt dV dt dV dt 24 T dt 24Tr 0 dr dt 24 r dr dh dt dt dr dt 127 dt Suppose that the radius is expanding at a rate of 0 8 inches per second How fast is the volume changing when the radius is 2 3 inches Use at least 5 decimal places in your answer second

20 Find an equation of the largest sphere with center 5 4 9 that is contained in the first octant

Based on the table what is the probability that there will be a cost overrun of 50 or more Between 20 and 30 Near what percent is the cost overrun most likely to be C y 20 0 01 0 10 0 08 0 19 10 0 32 20 0 50 The most likely amount of cost overrun is 30 40 50 Enter the exact answers for the probabilities Round your answer for the most likely amount of cost overrun to the nearest percent 0 80 0 94 0 99 The probability that there will be a cost overrun of 50 or more is 50 The probability that there will be a cost overrun between 20 and 30 is 99 30

Use properties of the indefinite integral to express the following integral in terms of the simplest integrals 3x 5x dx Select the correct answer below 3 3 x dx 5 3 x dx 3x dx 5 x dx 5x dx T x dx 3 x dx 5 xdx

61 If oil leaks from a tank at a rate of r t gallons per minute at 120 time t what does 1 0 r t dt represent

Use derivatives to determine which of the functions below is the anti derivative of 2 Select the correct answer below O 2 In 2 C Ox 2 C O2 C C

Use properties of the indefinite integral to express the following integral in terms of simpler integrals 2x 3x 3 dx Select the correct answer below 2 3 dx x dx 3 dx 2 x dx 3 xdx 30 0 2x dx 3 02 0 2 2 dx 3x dx 3 dx 1 3 dx 0 2 x dx 3 xdx 3dx 2 x dx 3 xdx 3dx 0 2 x dx 3 x dx

Evaluate the integral above by taking the derivative of each answer choice to determine which function is the antiderivative of 40xe5x Select the correct answer below O Ses C O4e25x C 4x5x C O4e x C

Solve the initial value problem y x 0 dy dx 1 10 y 16 0

6 Suppose the monthly revenue in thousands of dollars for the sale of xhundred units of an electronic item is given by the function R x 40x e 0 4x 30 Determine the number of units to produce in order to maximize revenue

5 Find the slope and equation of the tangent line to the curve f x sin x cos x at x

2 Determine the derivative of y 2x 3 3 8x Do not simplify

Solve the rational inequality graphically using a graphing calculator Give answers in interval notation If necessary round your answer to the nearest tenth 0 x 1 x x 5

25 54 Evaluate the integral S x 2x 4 dx 25 26 S x 100 dx

Differentiate y 12 log 5x d 12 log 5x dx

Find the integral 10 S 77 Ox dx

Find s t where s t represents the position function v t represents the velocity function and a t represents the acceleration function a t 6t 8 with v 0 5 and s 0 8 s t

10p b lim x 0 sin 3x cot 5x x cot 4x Do not use L Hopital s Rule

5 Find the area of the a u 2ij b u 8i 2j 3k v parallelogram that has two adjacent sides u and v 2k v 3i 2j k 2i 4j 4k

A pendulum of length 10 cm satisfies the equation 0 0 0 The bob is released from a starting angle 80 8 Find an equation for the position at any time and find the per of the motion g 9 8m s o k0 0 1 8 T T RT B

Section 4 2 Prove that if f is increasing then f a to illustrate this property f b f a b a for all ab Draw a picture

Find the inflection point for the function shown below If there are more than one be sure to spearate them by using a comma If there is not an inflection point record DNE in the answer box If necessary round all numbers to two decimal places f x 2x 18x 96x 3

Solve the inequality Enter your answer using interval notation x 2 x 3 X 1 X 2

Find the domain of the given function Enter your answer using interval notation 1 f x x482x2 81

Solve the inequality Enter your answer using interval notation x 1 x2 3 3 1 x 1

Find the global maximum and global minimum values of the function g 0 60 7 sin 0 on the interval 0 Use the derivatives to algebraically answer the question and leave answer in 4 decimal places The global minimum value The global maximum value H 0 3591 6 OF

Suppose 1100 square centimeters of material is available to make a box with a square base and an open top Find the largest possible volume of the box Give your answer rounded to the nearest whole cubic centimeter Volume 3510 57 cubic centimeters

The graph of f x 3 is reflected across the x axis shifted downward 8 units and then shifted left 3 units Let g x represent the new function What is an equation for this function g x What is the y intercept of g x Enter the answer as an ordered pair What is the domain of g x Enter the answer as an interval What is the range of g x Enter the answer as an interval help points help intervals help intervals help formulas

Graph f x 5x 1 1 First drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

The graph of f x 4 is shown below in blue This graph in red is a transformation of f x Write a function that describes the transformed function g x 6 2 0 f x g x

9 3 Problem 1 point The three series An Bn and Cn have terms 1 7210 C 2 3 Use the Limit Comparison Test to compare the following series to any of the above series For each of the series below you must enter two letters The first is the letter A B or C of the series above that it can be legally compared to with the Limit Comparison Test The second is C if the given series converges or D if it diverges So for instance if you believe the series converges and can be compared with series C above you would enter CC or if you believe it diverges and can be compared with series A you would enter AD n 1 5n5 n10 1309n15 9n5 5 5n 8n An 5n10 9n3 5 8n n 8n 9n 135n12 7 B 1 7257 C 1 1 n Hote To get full credit all answers must be correct Having all but one correct is worth 50 Two or more correct answers gives a score of 0

olve the following formula for the specified variable 1 2 gn m In gn cn for c O

Suppose an and bn are series with positive terms and bn is known to be divergent If an bn for all what can you say about an O A an diverges by Comparison Test OB an converges by Comparison Test C We cannot say anything about an

Follow the steps for graphing a rational function to graph the function R x 5x 5 8x 32 Write R x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice OA R x www Simplify your answer B R x is already in lowest terms Locate the intercept s of the graph Select the correct choice below and if necessary fill in the answer box es to complete your choice O A The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once B The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither x intercepts nor y intercepts 11

In each part find a formula for the general term of the sequence starting with 72 1 Enter the following information for an a an b an C d 11 5 1 1 1 3 9 27 1 1 9 27 2 8 26 80 3 9 27 81 0

Write the general formula for following alternating series in the form an 10 10 5 6 1 10 10 7 00

Write P x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice OA P x Simplify your answer B P x is already in lowest terms 36 Locate the intercept s of the graph Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once and no x intercept OC The graph has y intercept Simplify your answer Type an integer or a fraction D The graph has neither x intercepts nor y intercepts

Solve the inequality algebraically x 7 x 9 X 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numb expression

15 A 4v 17 2v 4m 4nm 1 B 42 D 2v 3 18 2x A 4x C x 18 2u y 3 2u A B B 3 x 2 1 2

Solve the inequality algebraically X 3 X 6 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbe expression

Solve the following inequality x 2 x 3 x 6 0

2 x 64x What is the solution Type your answer in interval notation Simplify your answer Use integers or fractions fo expression

Decide whether the following statement is true or false The graph of f x x x 0 or x 2 X is above the x axis for x 0 or x 2 so the solution set of the inequality X 2 Choose the correct answer below True False ww X x 2 20 is