Application of derivatives Questions and Answers

Stock prices are at their peak Here f is the stock price Then f x 0 f x 0 x 0 x 0 f x 0 f x 0 f x 0 f x 0 f x 0 f x 0

Match each function with its graph Function f x f x f x Graph Color a green b blue c red

Suppose that y f x is a differentiable function for which the following information is know f 2 1 f 2 1 5 f 2 0 25 Answer the following questions a Is f increasing or decreasing at z 2 increasing decreasing b Is f concave up or concave down at x 2 concave up concave down c Do you expect f 2 1 to be greater than 1 equal to 1 or less than 1 greater than 1 O equal to 1 less than 1 d Explain your reasoning in your answer to c

D Question 12 Give decreasing interval for f x x 1 5 x 6x

Question 11 use calculator to find Max point of f x x 15x 2 6x

Question 16 Find equation of the vertical f x 2x 3 x x 2

4 3 2 5 4 3 2 1 1 2 3 2 3 4 5 At the point shown on the function above which of the following is true O f 0 O f 0 O f 0

5 Of 0 Of 0 Of 0 3 At the point shown on the function above which of the following is true

Question 10 let f x x 5x find x h

Note 2 ALLY policy in Canvas Home pag D Question 1 IMM

The demand for a certain commodity is D p 5500e 0 02p units per month when the market price is p dollars per unit At what price does consumer expenditure E p pD p stop increasing and begin to decrease 2023 50 5500 O 61

math test is There are 6 colored pencils and 8 markers in Cameron s art bag Without looking Cameron chooses 1 item from the bag What is the probability that she chooses a colored pencil 6 14 to one decimal

Find an equation for the tangent line to y f x at the specified point f x 5xe x where x 0 y 5x o y 5ex y x y 5x

Find the second derivative of the given function f x 4e2x 9e x O f x 16e2x 9e x f x 16e2x 9e x f x 8e2x 9e x f x 8e2x 9e x

Differentiate the given function 3et f x 2x 3et f x 2 f x f x f x 3e x 1 4x 3xe 2x2 3e x 1 2x

Differentiate the given function f x 98 X 7 f x 81x89x 7 O f x 989X 7 f x 8189x 7 Of x 9x9 X 7

principal needed now to get 600 after 2 years at 12 co

amount that results from th vested at 3 compounded

Write an equation for the function graph 7 6 5 4 3 2 1 2 M IZ Li 2 4 5

he partial fraction decomposition of the giver 4 2x the partial fraction decomposition 4

Name MTH 161 Section 3 7 Graph Directions Sketch the graph of each function by han 5 2x 1 x a Find the y intercept L f x o Find the vertical asymptote

TUTU Write an equation for the function grap 3 4

Write the partial fraction decompos 5x 4 2 x 16x

O plify each of the following and 16 36 3

2 Vector A has a magnitude of 6 feet and forms an angle of 25 with the horizontal What is the magnitude of the vertical component a 1 5 feet b 2 5 feet c 5 4 feet d 7 0 feet

A leaf falls 18 feet from a branch to the ground at a rate of 5 feet every 2 seconds Determine whether each statement about the leaf is true Select True or False for each statement The leaf is 3 feet above the ground after 6 seconds 2 the leaf falls at a rate of foot every 1 second 5 The leaf is located 18 feet off the ground

The table below gives the annual sales in millions of dollars of a product year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 277 297 313 309 297 277 213 249 309 Determining the average rate of change of sales is important It tells whether sales are increasin decreasing over a time period and at what rate a What was the average rate of change of annual sales between 2003 and 2004 millions of dollars year b What was the average rate of change of annual sales between 2003 and 2005 millions of dollars year

Choose the situation that has the greatest rate of change A sunflower that grows 2 inches every day or an amaryllis that grows 18 inches in one we Sunflower Amaryllis ON

This graph shows a proportional relationship between the distance traveled by Tim on a road tri and the number of hours for which he traveled Distance Traveled by Tim Distance mi 250 200 150 100 50 4 6 8 Number of hours The slope of the line is Q Which statement identifies the correct slope and the correct interpretation of the slope for this situation The slope of the line is The slope of the line is x The slope of the ling in 10 50 so the distance traveled by Tim is 1 mile every 50 hours 1 1 so the distance traveled by Tim is 1 mile every 50 hours 50 50 so the distance traveled by Tim is 50 miles every hour 1 1

The instantaneous rate of change at a point is equivalent to The slope of a secant line through that point The slope of the secant line between that point and the next one The slope of the tangent line at the point The slope of a horizontal line near that point The slope of the secant line between that point and the previous one

Sketch the region bounded by y 2 x 1 y 3 x 1 and x 2 and find its area Choose the correct graph below OA G The area of the region bounded by y 2 x 1 y 3 x 1 and x 2 is Simplify your answer CCTED OC Q Q

F t 2 t i 61 7t k in meters Determine the length of the trajectory if 0 t 3 2 De

A team of researchers is testing the effectiveness of a new HPV vaccine They randomly divide the subjects into two groups Group 1 receives existing HPV vaccine and Group 2 receives new HPV vaccine The patients in the study do not know which group they are in Which is the treatment group Group 1 Group 2 Neither group Which is the control group if there is one Group 1 Group 2 No control group Is this study blind double blind or neither Blind Double blind Neither Which best describes this research Placebo Controlled Experiment Survey Controlled Experiment Clinical Study O CO

Suppose f 5 0 5 4 and all functions are continuous f x lim z 5 g x g 5 0 g 5 1 C

Determine the volume and the sur Use the key on your calculator The volume is Simplify your answer Type an int drodth as needed

e inverse of the one to one fur 13 10 4 9 6 3 10 1

e data given below represent the expected percentage of putts that will be made by professional golfe pending on distance For example it is expected that 99 1 of 2 foot putts will be made Using a grap scatter diagram of the data with distance as the independent variable Complete parts a through d Distance Expected Percentage feet 2 3 99 1 94 3 Question 7 6 9 11 Part 2 of 4 Distance feet 14 15 Expected F 26 22

v t of an object of mais M in freefall satisfies a differential equation frac d e dt frac k M left v frac M cdot g k right Where 9 9 8 k m is the constant acceleration due to gravity and m is the air tesistance constant tecminal velocity mph Note Answer should be negative for downward velocity

b The volume of ice cream bounded by the cone z x y 2 and the sphere x y z 16

A region is bounded by the parabola z y and the line ry The area of the region can be calculated as Select one a b C Ldxdy Lo L dydz dydz O d dydz 0

The engine in a car has eight cylinders engine Use the button on your calcula

After helping your friend with her new home you want to continue putting your Survey of Math knowledge to work A local charity is having their annual fundraiser and wants your help with some of the organization of the event and the games Marble Games Using some leftover marbles from an old game you create a bag of 9 marbles 6 blue 2 green and 1 red The three games below all use this bag of marbles Two of the Marbles Two marbles are drawn out of the bag without replacement If two green marbles are drawn the player wins 18 If a red marble is drawn with either the first draw or the second draw the player loses 4 50 the cost to play Otherwise the player breaks even Three of the Marbles Three marbles are drawn out of the bag without replacement If at most two blue marbles are drawn the player wins 7 Otherwise the player loses 14 the cost to play All of the Marbles Three marbles are drawn out of the bag with replacement If at least one red marble is drawn the player loses 2 the cost to play Otherwise the player wins 70

Answer parts a e for the function shown below f x x 3x x 3 a Use the leading coefficient test to determine the graph s end behavior Which statement describes the behavior at the ends of fix x 3x x 37 A The graph rises to the left and to the right OB The graph rises to the left and falls to the right OC The graph falls to the left and rises to the right OD The graph falls to the left and to the right fo ka 40 IA 14

110 teras 15 CO HOT NO Kty MaH www KIN H 3 M C K 6 INS CO 6 10 Solve the following inequality g w 0 2 1 F X Os

Drew s monthly net income is 1 300 What is the maximum he should use on debt payments Maximum monthly debt payments LA 468

Let f x 5x 11z 4 f x h f 1 h enter the expression needed to find the derivative at z 3 Using the definition of derivative f x lim h 0 f x lim h 0 After evaluating this limit we see that x df dz Finally the equation of the tangent line to f z where z 3 is

The graph of a function follows 4 8 Choose the graph of its derivative from among the following functions 20 1010 8 8 4 8 O 8 4 FERR M N 8 4 8 O 4 8 4 8 O

5 4 3 2 1 f 2 3 3 0 CN 2 te 2 3 54 De 2 3 Use the graph of f x above to estimate the value of f 2 to one decimal plac 456 X 5

Given f x 5x 5x 2 find x using the limit definition of the derivative x

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