Differentiation Questions and Answers

3 Draw a graph Showing with the following information 1 Curver should be Concave up 1 be intercepts be 2 and 9 11 y intercepts 4 Should be 1 choose the value of minima as per your firsl understanding

2 Use the graph below to find the average rate of change AROC Temperature F 1600 1200 800 400 0 1 5 900 2 5 1300 1 700 5 1640 2 4 6 Time hours a Find the average rate of change from 0 to 2 5 hours 8 1800 8 b Find the average rate of change from 1 to 8 hours c Find the average rate of change from 1 5 to 4 hours d Find the average rate of change from 1 to 5 hours 10 e Find the average rate of change on the interval 1 5 2 5

Use Taylor s Theorem to obtain an upper bound for the error of the approximation Then calculate the value of the error Round your answers to three significant figures 0 7 3 3 sinh 0 7 0 7 R 0 0502 R 0 0014

27 30 Circular Motion The position of an object in circular motion is modeled by the given parametric equations Describe the path of the object by stating the radius of the circle the posi tion at time 1 0 the orientation of the motion clockwise or counterclockwise and the time that it takes to complete one revolution around the circle 27 x 3 cos y 3 sint 29 x sin 21 y cos 2t 28 x 2 sint y 2 cost 30 x 4 cos 3t y 4 sin 31

if I 1 2 1 if 1 f x Graph the function Note Be sure to include closed or open dots but only at breaks in the grap Arrows are assumed if no end symbols are shown 10 9 OD N 8 7 65 4321 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 1234 2 3 S 6 5 6400 as 7 8 9 10 9 10

Consider the matrix A A Write the general solution of the system x t Ax e in matrix form x t X t e Enter each matrix in the form row 1 row 2 J where each row is a comm t

Problem 1 The density p x in cars per mile was recorded in the table below at various points along an eight mile road between a major city and a traffic collision Approximate the total number of cars on the eight mile road using a midpoint approximation with n 4 I 0 1 2 3 4 5 6 7 8 p x 225 200 275 250 325 500 659 400 650 CITY collision

Find the inverse of the following matrix if possible Reduce all fractions to lowest terms B1 Answer A Selecting an option will display any text boxes needed to complete your answer Does this matrix have an inverse Yes No

Write the following system of equations as a single matrix equation 5z 8x 0 3y 10 7z 4x 3y 4 0

The government has decided on a tax rebate program to stimulate the economy Suppose that you receive 1400 and you spend 90 of this and each person who receives what you spend in turn spend 90 of what they receive and this process continues indefinitely What is the total amount spent to the nearest dollar that results from this government action Total amount spent

4 A B 3 LO X 1 2 65 2 Determine the dimensions of AB

A 1 2 4 A B 8 0 1 2 5 3 B 7 3 2 1 0 8 0 3 5

Find polar coordinates of the point that has rectangular coordinates 3 2 Write your answer using degrees and round your coordinates to the nearest hundredth

7 Convert the angle 6 radians to degrees rounding to the nearest 10th

Fill in the blank to make a true statement sec x 1 help formulas

Find dy dx by implicit differentiation x 5y 7 454 10y x2 7 10y

Find the derivative of the function y In 8x x O8x 2 8x2 x O 24x 2 8x2 O 24x 2 8x3 x

Find the relative extrema of the function if they exist f x 2x 12x 17 O Relative maximum at 3 1 Relative minimum at 3 1 Relative minimum at 1 3 O Relative minimum at 1 3

Solve the exponential equation for t Round your answer to three decimal places if necessary e t 0 05 0 136 0 018 2 996 2 996

Your business requests a 3 month loan for 450 000 What will be the interest paid at the end of the term if the business risk percentage is assessed at 2 2 and LIBOR is at 1 8 interest paid Round to the nearest hundredth

Calculate the Inverse of the following Matrix with Gauss Jordan method 1 0 5 0 51 3 3 A 4 3

Express 2 1 x3xZ in the form x What is the value of s

7000 1 999e Step 2 of 2 How many people have caught the flu after 4 weeks Round to the nearest person The function models the number of people in a small town who have caught the flur weeks after the initial outbreak

Jerod hopes to earn 1200 in interest in 4 4 years time from 48 000 that he has available to invest To decide if it s feasible to do this by investing in an account that compounds daily he needs to determine the annual interest rate such an account would have to offer for him to meet his goal What would the annual rate of interest have to be Round to two decimal places

Darin is saving up money for a down payment on a car He currently has 5450 but knows he can get a loan at a lower interest rate if he can put down 6242 If he invests the 5450 in an account that earns 4 7 annually compounded continuously how long will it take Darin to accumulate the 62427 Round your answer to two decimal places if necessary Keypad

uppose the internal temperature of a building is modeled by y 5 sin x 10 75 where s the number of hours since midnight At two times during the day the temperature is exactly 78 Find those two times Note A time such as 13 45998 should be given as 1 27 pm because even though 0 459986027 5 is closer to 28 than it is to 27 clock time doesn t round

How do you graph the polar curve r 6 sin 0 Drag an equation variable or phrase into each box to correctly complete the statements Consider the graph of L curve will be symmetric about same as the values of the function Translate ordered pairs from this function to polar coordinates and plot these points The 3003 f x 6 cos I f x 6 sin z r 0 The circle with a radius of 6 8 0 Its shape is a cardiod values of the polar curve are the 0 5 rose with 6 petals limacon with an inner loop circle with a radius of 3

5 find a Cartesian equation for r 6 c0s 0 Graph it X Y COSA x 60050 050 y Goosa vey Colo X 6cos 0 4 6030

4 15 cos x y if sin x 54 5 COS X sin y and cos y 11

3 16 tan x y if tan x tan y 55

Find the partial derivatives of the function fx x y f x y f x y 7x 9y 2x 6y

For this graph What is true about the graph at point P Choose all that are correct Increasing Decreasing Continuous Discontinuous Concave up Concave down Inflection Point Differentiable Nondifferentiable Has a limit at x P The limit at x P does not exist Has a derivative of 0

12 Use the Mean Value Theorem f c equals the average slope a f x x on the interval 0 2 f b f a b a to find value for c where the instantaneous slope

You were asked to find u 5v given the following vectors u 6 9 v 1 3 Finally complete the addition or subtraction and enter your answer in the boxes below u 5v 6 9 5 15 u 5y

Find a parametric description for the given oriented curve the directed segment from 10 1 to 10 3 0 t 1

A grocer wants to mix two kinds of candy One kind sells for 0 90 per pound and the other sells for 1 50 per pound He wants to mix a total of 19 pounds and sell it for 1 00 per pound How many pounds of each kind should he use in the new mix Round off the answers to the nearest hundredth Answer How to enter your answer opens in new window number of pounds of candy that sells for 0 90 number of pounds of candy that sells for 1 50 Keypad Keyboard Shortcut

Find f x y 24x 12y Answer format Enter the value hint use if needed Congratulations your answer is correct and saved Check Answer Save Step By Step Example Find f x y 3y 12x Answer format Enter a number hint use if needed Congratulations your answer is correct and saved Check Answer Save Step By Step Example Se Live Help Live Help and f ry 0 and solve the equations

Check Answer Save Answer format a b c A direction vector A vector perpendicular to the line A point on the line Step By Step Example Find the point associated with x y 2 3 on the surface generated by x y z where z f x y 2 3 22 Check Answer Save O Step By Step Example Answer format a b c Live Help For fixed y 3 the tangent vector direction vector is given by the derivative of x y f x y with respect to x find the 1 0 16 Congratulations your answer is correct and saved Check Answer Save Step By Step Example Live Help Live Help What is the equation of the tangent line to the trace of y 3 2 1 3 22 16t Answer format a bt c dt e ft where a b c d e and f are constants and is the parameter

dz Givenz f x y xy x cosy and x and y 2 find dr The chain rule is Find of Au di B di di di II 11 Congratulations your answer is correct and saved Check Answer Save Step By Step Example df dx dx de of dx Ox di dx dx of df dy dy di of dy of of dy dy di of dx dy di Live Help

ind the equation of a line in 3D what do you need Slope of the line in traditional sense A direction vector A vector perpendicular to the line A point on the line Check Answer Save swer format a b c Step By Step Example d the point associated with x y 2 3 on the surface nerated by x y z where z f x y 2 3 22 Check Answer Save Live Hel Step By Step Example Live He

Find and classify all the critical points of the function f x y x 2 2y 2 4x x 2 y 3

7 Explain how you would graph the following set of parametric equations by plotting points describing the orientation x 3t and y 1 Eliminate the t from x 3t I

a Sketch the graph of f x on the graph of f x given below

14 Find a formula for in terms of x and y given that y is given as a function of x implicitly by the formula 2y x 24 xy 8 8x

1 Let f x be defined as below What value s of k would make the function continuous x x 12 f x x 9x 18 kx 2 x 3 x 3

Find the derivative of each of the following functions 1 7 2 x 1 y 2x 5 3x

Find the energy released when 82X211 atomic mass 210 98874 u undergoes 8 decay to become 83X1215 atomic mass 210 98726 u Number M Parent nucleus N Z Units Daughter nucleus N 10 Z 1G B particle electron

g tan 1 O Suppose f 1 where g is a function and inside O is an expression in terms of t Find f 1 and show 1 how you set up the problem 2 each step and 3 the name of differentiation rules that you used Type your answer in the space provided 1 0

Tuppose f 1 sin 40 where inside O is a function of 1 Find f 1 and show 1 how you set up the problem 2 each step and 3 the name of differentiation rules that you used Type your answer in the space provided

If we know that g 0 10 and g 0 3 find the numerical value of f 0 where e x g x 2 e f x