Application of derivatives Questions and Answers

Find an equation for the family of linear functions such that f 6 5 a f x 5 m x 6 b f x m x 5 5 c f x 6 m x 5

A caterer offers a package that feeds up to 50 people for 1 500 and adds an additional charge of 24 75 for each additional person Enter a linear model that represents the total amount charged a host t as a function of g the numbe additional guests Provide your answer below

day care center invests 25 000 to set up a new facility The center plans to charge 550 per student per year Write a near model in the form y mx b where y represents the amount of profit the center earns for enrolling x number of tudents

d if the relation is a function 1 8 1 4 5 1 The relation is 2 Range 3 Domain 6 a 8 3 1 0 b 3 0 6 c 3 4 5 d a function e 8 3 4 f not a function g 8 1 4 5 h 3 0 6 6

Find the area of the shaded region 12 8 T 0 9 0 7 0 3 0 1 0 5 0 9 y st 4 2x 2 X 2 8 10

A submarine is at the surface of the ocean It begins its descent at a rate of 100 feet per minute Write a linear model in the form d t mt b where d t represents the depth of the submarine relative to sea level in feet after t minutes into its descent Be sure to include d t in your answer Note when the submarine is below sea level its depth is a negative quantity holour

3 Simplify the following expressions x 1dx 10

4 Find the area of the region bounded by the graph off and the s axis on the given interval f x x 1 on 1 2

uestion David and Amy start at the same point and begin biking in different directions David is biking west at a spee per hour Amy is biking south at a speed of 15 miles per hour After how many hours will they be exactly 23 miles apart Round your answer to two decimal places Provide your answer below

Two elevators at different heights start to descend at the same time but at different rates Assume the heights are changing linearly After how many seconds will the elevators be at the same height Elevator s Height ft Time sec Elevator A Elevator B 27 23 21 Provide your answer below 1 3 19

Find the value of f 25 if f t 8 t 25 3 t

In 1979 the number of high school dropouts in a country was 5216 thousand By 2007 this number had decreased to 3120 thousand Find and interpret the average rate of change per year in the number of high school dropouts CIE Select the correct choice below and fill in the answer boxes to complete your choice Round to the nearest tenth as needed OA The average rate of change is about decreased by an average of about OB The average rate of change is about decreased by an average of about OC The average rate of change is about thousand each year The number of high school dropouts thousand each year from 1979 to 2007 thousand each year The number of high school dropouts thousand in the year 2007 thousand each year The number of high school dropouts increased by an average of about thousand in the year 2007 OD The average rate of change is about thousand each year The number of high school dropouts increased by an average of about thousand each year from 1979 to 2007

Consider the function f x 3x 3x 2 and complete parts a through c a Find f a h b Find c Find the instantaneous rate of change of f when a 6 f a h h a f a h 3a2 3h 3ah 3a 3h 2 Simplify your answer Do not factor f a h f a b h Simplify your answer Do not factor c The instantaneous rate of change of f when a 6 is Simplify your answer

The fourth term of 3x 5y 6 is A 11 390 625x y B 67 500x y C 300x y4 D 2700x y OA OB OC

Find the derivative of the following function dr ds 11 1 2s 8 4 5s

D Question 4 The second term of 2x y is A 32r y B 4x y C 16xy D xy OA OB 1 pts O C

Find the equation of Give your answer in slope intercept form y mx b the line with slope 2 which goes through the point 9 7

Use the binomial theorem to expand 2x y A 16 r 32r y 24r y 8xy y B 2r2r y 2x y 2xy y C 27 4r y 6x y 2xy y D 16r 32r y 24x y 8xy y OA OB OC OD

How many terms are in the expansion of a 5 b 8 O A OB O C OD 2x 3y 2 c 7 d 6

Find the equation of the line with slope and y intercept 0 2 Write the equation in standard form

There are two numbers which add up to 17 If one number is 13 more than the other find the two numbers Provide your answer below

Find the equation the linear function whose graph is given here Use the letter x in your answer rather than multiplication symbol Provide your answer below 654321 6 4 3 2 7 6 5 4 3 2 11 1 2 3 4 5 6 7 2 1111 T 4567 4 7

Suppose f x x 3 e x 4 x 1 or PDF of your solution Show your work and Include all the details in your solution Write the conclusions clearly Draw a table and use it to determine the intervals of increase and decrease of f and the location of its local maxima and minima

Find the equation of the linear function whose graph is given here Use the letter x in your answer rather than the multiplication symbol 4325 7 6 5 4 3 2 11 1 3 4 5 6 7

Determine the convergence or divergence of the series and identify the test used DO n 1 O diverges by the Geometric Series Test O converges by the Limit Comparison Test O diverges by the Limit Comparison Test O converges by the Geometric Series Test 1 47 2

sin 2t cos 2t dt True 1 12 Click here to view the transcript sin 2t C

Simplify the expression and express the answer using rational exponents Assume that u and v denote positive numbers 4u v3 u v7 2u 1 2 S

Find the limit 2 lim 848 4x6 4x x x 2

Click here to view the transcript Taylor s theorem generates a power series from a function using the formula f x n 0 O True f n c x c n

The interval of convergence for O True Click here to view the transcript False 8 n 0 1 x 1 27 is 3 x 1

Find the nth Maclaurin polynomial for the function f x e x n 5 Ps x

Find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration 13 1 x 9x 16 dx 3 3 in esc tan cot tan

Step 3 Recall the Pythagorean identity which states that 1 tan u sec u Using this Pythagorean identity simplify the denominator 18 18 sec x 1 Step 5 Step 4 Rewrite the expression 18 tan x 18 2 tan x 18 Finally use the Reciprocal identity 1 1 tan x tan x cot x to simplify the expression

Step 1 1 The given improper integral is Therefore If f is continuous on the interval 0 0 dx So e x e 7x lim B18 Jo e7x 1 e x e 7x dx The given improper integral converges if the limit exists otherwise it diver 1 Step 2 Simplify the right side of the expression dx lim b18 dx lim b 0 b 1 e7x e 7x 7 x INFINITY 7x 2 dx 71 e e14x 7 then 1 Step 3 Apply the Arctangent Rule for Integration on the right side of the expression rb 7x dx 16 lim f x dx lim f x dx

Find the indefinite integral 1 Step 1 xex 7x 1 To find the integral Let dv V dv 7x 1 dx and integrate the differential equation to obtain the function v xe 7x 1 1 7x 7x 1 dx use the formula of integration by parts 1 2 dx LEK 2 dx

Evaluate the definite integral using the given integration limits and the limits obtained by trigonometric substitution 1 2 1 2 3 2 a the given integration limits dt b the limits obtained by trigonometric substitution

B D What substitution should be applied in order to solve binomial integral x 1 x dx 1 x 3 t x1 3 1 x 2 t6 x t 1 x 3 t

vThe following ordered pairs model a linear function rule 2 9 1 7 0 5 1 3 2 1 Which ordered pair can be added to the given set and still have the set represent the same linear function

Determine whether or not the function is continuous for the given values of x x 1 f x X 8 x 0 x 8 x 1 OA Yes the point is defined lim f x exists and lim f x Simplify your answer X C X 0 Is the function continuous at x 0 Select the correct choice below and if necessary fill in the answer box to complete your che OA Yes the point is defined lim f x exists and lim f x Simplify your answer X C X 8 OB No the function is not continuous at x 0 Is the function continuous at x 8 Select the correct choice below and if necessary fill in the answer box to complete your choi This q OA Yes the point is defined lim f x exists and lim f x Simplify your answer X C X 1 OB No the function is not continuous at x 8 Is the function continuous at x 1 Select the correct choice below and if necessary fill in the answer box to complete your chc B No the function is not continuous at x 1

Find the derivative of the function 314 f x 12 x 16x

Use a calculator to estimate the limit x 81 2 X 9 lim X 0 A 18 OB 0 OC 9

I need to sove this equation with f x being f a h G 10 f x x 71 8

Find the x intercept of the following line 9 Provide your answer below y Leave coordinates as fractions if necessary Give your answer as an ordered pair a b 1

Officials in a particular state have raised and lowered the state sales tax in various years as hown in the accompanying figure Let T x represent the sales tax rate as a percentage in year E Find the given quantities IT X 8 7 5 7 6 5 6 5 5 5 6 4 5 4 3 5 2001 2005 2009 2013 2017 Year Q Q Select the correct choice below and if necessary fill in the answer box to complete your choice A OB d Find lim T x x 2017 lim T x 7 5 x 2008 Type an integer or a decimal Select the correct choice below and if necessary fill in the answer box to complete your choice A lim T x does not exist x 2008 OB lim T x 6 x 2017 Type an integer or a decimal e Find lim T x does not exist x 2017 lim T x X 2017 3 Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim T x x 2017 Type an integer or a decimal

1 Graph of a function is shown a If this graph shows y f x what are the x coordinates of critical numbers of f x b If this graph shows y f x what are the r coordinates of critical numbers of f x Answer a x 2 5 2 1 5 0 2 b x 3 2 1 2

A manufacturer reports the following Sales Variable cost of goods sold Fixed overhead Variable selling and administrative expenses Fixed selling and administrative expenses Compute the contribution margin ratio 600 000 200 000 160 000 70 000 50 000

Quiza QI find the following a sin 240 3 6 ton 270 Sin 2700 012760 etus d Tlo

A study of the demand for air travel between two cities depends on the airfare according to th following demand equation q 55 6 0 022p a Find the elasticity when the price is 166 53 E Round to the nearest thousandth as needed b Is the demand for airfare elastic or inelastic at this price The demand for airfare at 166 53 is 1 c Find the price that maximizes revenue Revenue will be maximized when the price is Round to the nearest dollar as needed 1 O inelastic O elastic

2 COMPUTE EACH MATRIX SUM OR PRODUCT IF IT IS DEFINED IF AN EXPRESSION IS NOT DEFINED EXPLAIN WHY 0 7 5 4 2 34 B 5 1 1 2 A 3 D 1 1 E 4 C 2 1 2A B 2A AC CD 2 A 3B 2C 3E DB EC

Given the function f x whose graph is shown below determine f 2 I Do not include f 2 in your answer Provide your answer bolour f x 2 0 2 0 2