Application of derivatives Questions and Answers

Starting with the graph of a basic function graph the following function using the techniques of shifting compressing stretching and or reflecting Find the domain and range of the function g x 5 x 4 2 Use the graphing tool to graph the equation Click to enlarge graph 10 B 6 4 2 10 8 6 2 2 4 6 2

Next question Get a similar Suppose that f is a function given as f x 7x 5 We will compute the derivative of f at x 3 as follows First we will compute and simplify the expression f 3 h f 3 h Then we compute and simplify the difference quotient between x 3 and x 3 h f 3 h f 3 h The derivative of the function at x 3 is the limit of the difference quotient as h approaches zero f 3 h f 3 h f 3 lim h 0

8 Next question 6 4 10 8 6 4 2 2 4 6 Clear All Draw Dot Get a similar question Line Segment 8 You can a Mark the two points on the graph that are needed to calculate Average Rate of Change over the interval 4 1 b Connect the points with a line segment c The Average Rate of Change over 4 1 is positive negative

2 12 pts Describe the domain of function g using set builder and interval notation g t 4 11 3t 8t 2t 15

the functions below to answer a through e f x 3x 5 a f g x a 3x 5 27 10 2x 3x 15 d gof x g x 2x 10 b h g x 9 3x 5 2 2x 5 2 0 2 2 4X 30X 25 10 e foh x h x 5x 3 c h f x 3X 5 5X 3 3x 5 5X 3 2x 8 b

Verify if the functions are inverses Show using function composition fog x x and gof x x f x 3x 2 g x 2 a fog x b gof x

In June 2000 in the US there were 9135 wildfires that burned a total of 606 869 acres Convert these numbers to a unit rate of acres per fire Round your answer to the nearest tenth one decimal space

Determine whether the following series converges or diverges Input C for convergence and D for divergence Determine whether the following series converges or diverges Input C for convergence and D for divergence 7 Note You have only two chances to enter your answer 6 cos n 6n 3 4 4

D casch 13 V10 Find the other the trigonometrte ration of 10 10

12 16 Points Sketch a triangle that has acute angle cace COS 0 tan en DETAILS sec 0 con e 14 14 2 33 Find the other five trigonometric ratios of si 14 44 2 33 2V 63 O ZV 33 2165 2 33 14 14

60 For what value of x does the graph of f x e 2x have a horizontal tangent

Sketch a triangle that has acute angle COS 2 GOU SCD UI tantel Find the other the trigonometric ratios of t drid THE NM 3 3 D VA 2 2

Find the side labeled x X X 60

A cardiac monitor is used to measure the heart rate of a patient after surgery It compiles the number of heartbeats after t minutes When the data in the table are graphed the slope of the tangent line represents the heart rate in beats per minute t min 36 38 40 42 44 Heartbeats 2505 2640 2773 2906 3042 The monitor estimates this value by calculating the slope of a secant line Use the data to estimate the patient s heart rate after 42 minutes using the secant line between the points with the given values of t Round your answers to one decimal place a t 36 and t 42 67 8 x b t 38 and t 42 67 25 X c t 40 and t 42 66 5 d t 42 and t 44 69

3 34 Differentiate the function 3 g x 4x 7 5 f x x75 x 3 7 f t 2e

List the interval s on which f is decreasing The interval s on which f is decreasing is are 9 7 0 1 3 6 Type your answer in interval notation Use a comma to separate answers as needed 4 14 12 14 10 4 Ay

Complete the sentence below 2 The function f x x is decreasing on the interval 2 The function f x x is decreasing on the interval 0 00 00 0 00 0 00

Use similar triangles to solve A person who is 6 feet tall is standing 120 feet from the base of a tree and the tree casts a 130 foot shadow The person s shadow is 10 feet in length What is the height of the tree The height is in yd C 120 ft 6 ft 10 ft

8 12 11 U 19 find 12 9Find f 0 the graph of f x shown 10 Solve f x 0 11 Find f 0 12 Solve f x 0 13 Sketch f x 12 Using the graph shown a Find g 1 b Solve g x 1 X f x c Find g 1 d Solve g x 1 e Sketch f x t h t 13 Use the table below to find the indicated quantities 0 1 2 3 7 1 14 Find f 7 15 Solve f x 4 16 Find f 8 17 Solve f x 2 3 9 a Find h 3 b Solve h t 5 c Find h 0 10 4 6 14 Use the table below to fill in the missing values 0 1 2 3 4 9 4 7 2 5 10 If 1 7 find 1 5 2 2 3 2 1 f x 1 2 3 5 1 6 8 g x 2 3 6 8 7 5 4 7 0 8 0 9 4 8 3

5 ind a formula for the inverse function that gives Fahrenheit temperature given a Celsius 9 temperature If F h C 32 C then C h F 5

The rectangular tank shown here with its top at ground level is used to catch runoff water Assume that the water weighs 62 2 lb ft a How much work does it take to empty the tank by pumping the water back to ground level once the tank is full b If the water is pumped to ground level with a 5 11 horsepower hp motor work output 250 ft lb sec how long will it take to empty the tank to the nearest minute c Show that the pump in part b will lower the water level 15 ft halfway during the first 42 minutes of pumping d What are the answers to parts a and b in a location where water weighs 62 07 lb ft 62 36 lb ft a Set up an integral to find the work done W How much work does it take to empty the tank b How long will it take to empty the tank minutes Round to the nearest minute as needed c How much work does it take to lower the water level halfway t will take the pump minutes to do this work so the pump Round to the nearest minute as needed In a location where water weighs 62 07 lb ft it will take a location where water weighs 62 36 lb ft it will take TE lower the water level halfway during the first 42 minutes of pumping of work to empty the tank and it will take of work to empty the tank and it will take minutes to empty the tank minutes to empty the tank Ground level 6 ft 0 30

btract Simplify by collecting like radical terms if possible assuming that all expressions under radicals represent non negative numbers 54x 3 2x4 54x 3 2x 3 2x x 2x Simplify your answer Type an exact answer using radicals as needed

Simplify by taking roots of the numerator and denominator 64 81 64 81 Type an exact answer using radicals as needed

4 2 0 a b c e 2 lim f x 2 2 d f 2 lim f x 2 2 lim f x 2 2 4 lim f x x 4 f f 4 AX

a b c d 3 lim R x 12 lim R x 215 lim 113 R x lim R x 2 3 2 5 AR e The equations of the vertical asymptotes In order from left to right

Multiply and simplify by factoring Assume that all expressions under radicals represent nonnegative numbers 3 13 3 vy 3 14 13 3 16y 14 Simplify your answer Type in radical form vy 16y

The three series A B and C have terms 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 2 3 888 n 1 9n n 9n 4n10 3n9 9 3n 9n6 An 7 Br Cn zz n5 n 5n7 4n 5 5n5 n 1683n12 4n5 3

Simplify by factoring Assume that all expressions under the radical represent nonnegative numbers 405x y 46 46 405x y Type an exact answer using radicals as needed

Simplify by factoring 28 28 Type an exact answe

Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test If at least one test can be applied to the series enter CONV if it converges or DIV if it diverges If neither test can be applied to the series enter NA Note this means that even if you know a given series converges by some other test but the comparison tests cannot be applied to it ther you must enter NA rather than CONV 3 4 5 DO n 1 n 1 DO n 1 WW 22 DO n 1 8n5 n6 3 cos n n 8n 3 8n5 n 3 5n8n6 8 n 9n 10 n5 5 cos n n n5

f x 1 4x for x 0 x 3 for x 0 Choose the correct graph below OA 0 Ay 10 O B O C 10 10 110 Q O D 10 10 2

Which of the following expresses the area of the garden as a function of the length OA A x 28x x OB A x 28x x OC A x 14x x 2 OD Axl ter 2

For the piecewise function find the values g 1 g 1 and g 2 g x x 9 for x 1 3 x for x 1 9 1 0

Determine the intervals on which the function is increasing decreasing and constant List the interval s on which the function is increasing 6 1 0 Type your answer in interval notation Use a comma to separate answers as needed List the interval s on which the function is decreasing 6 4 Type your answer in interval notation Use a comma to separate answers as needed List the interval s on which the function is constant Type your answer in interval notation Use a comma to separate answers as needed Ay 16 G

Graph the piecewise function on the right Choose the graph of the piecewise function below O A OB o 17 O C 10 Ay f x 4x 2 for x 1 5 1 for 1 x 4 for x 4 O D 104 Q

Click the Secant Line Slope of Secant and Values boxes Set the x slider to the point x 4 5 and the x h slider 5 Complete parts 1 through 3 below Use the interactive figure to find your answer Use the left and right arrow keys to move along a slider as needed Click here to launch the interactive figure BECKH Part 1 What is the slope m of the secant line when x 4 5 and h 0 5

2 g x x 1 4 Graph the function g if x 3 if 3 x 3 if x 3 1 X O

question Taking logarithms and antilogarithms is necessary to solve many chemistry problems For practice complete the following table where N is a number N log N 8 86 In N 4 449

1 point The table below A f d the amount of money A in billions of dollars in bills of denomination d circulating in US currency in 2005 For example according to the table values below there wer 60 2 billion worth of 50 bills in circulation a Find f 50 60 2 b Using your answer in a what was the total number of 50 bills not amount of money in circulation in 2005 There was a total number of 50 billion 50 bills in circulation c Are the following statements True or False False False V 1 There were more 1 dollar bills than 5 dollar bills Denomination value of bill 1 5 10 20 50 100 Dollar Value in Circulation 8 49 7 14 8 110 160 2 524 5 2 There were more 5 dollar bills than 10 dollar bills

Similar question You can retry this question below A bungee jumper dives from a tower at time t 0 Her heights in feet at time t in seconds is given by 0 2t s t 300 cos 0 75t e 300 a Write an expression for the average velocity of the bungee jumper on the interval 1 1 h AV 1 1 h Use computing technology to estimate the value of the limit as h 0 of the quantity you found in a lim AV 1 1 h h 0 feet per second What is the meaning of the value of the limit in b What are the units The instantaneous velocity of the bungee jumper at the moment t 1 is approximately

On what domain is the function f x x 3x 4 1 x 1 continuous

f x Get a similar question x 6x 5 x2 3x 4 f 5 lim f x x115 f x f x is continuous lim f x x 5 Add Work 0 You can

Use the figure below which gives a graph of the function f x to give values for the indicated limits Enter NA if a limit does not exist 2 8 a lim f x b lim f x c lim f x d lim f x 6 4 2 6 8 10 1 O 2 3 4 O 5

Calculate the gradient of h x y z x 2 Vh 3x 4yz3 x 3z3 3yz2 Answers Attempt 8 of 8

Find the curvature of x t y 2t3 at the point 1 2 Round your answer to 4 decimal places 7 points

4 Find the exact value of t such that r t 5 if r t 4et 5 6e t 7 points

For each statement choose TRUE or FALSE No work needed 2 points If k t 0 for all t then the curve is a straight line TRUE FALSE If u xv 0 then u 0 or v 0 TRUE FALSE

Here is a contour plot of the function f a 4 3y Click the image to enlarge it By looking at the contour plot characterize the two critical points of the function You should be able to do this analysis without computing derivatives but you may want to compute them to corroborate intuition The critical point 1 1 is a local The second critical point is at the point choose one from the list and it is a saddle point 0

Given the graphs of f x and g x find g f 4 5 0 5 f x g x

Find the maximum rate of change of f 2 2 3 2 at the point 4 4 1 and the direction in which it occurs Maximum rate of change Direction unit vector in which it occurs