Calculus Questions

For f x 2 x 2x 3 x 2 determine the x intercepts and the end behavior Enter intercepts as a comma separated list of points Intercepts help points As x f x As x o f x help numbers help numbers

Find the intercepts of f x 2 x 5 x 5 x 3 Enter intercepts as points If you have more than one point enter them as a comma separated list help points y intercept x intercept s help points

83 An office lamp manufacturer has weekly revenue and cost equations both in dollars given by R 38x 0 1 x and C 5x 2000 respectively where x is the number of lamps made and sold each week If the number of lamps made and sold is increasing at a rate of 30 lamps per week find the rate of change of the company s profit with respect to time when 200 lamps are made and sold each week Interpret your answer

87 A manufacturer determines the relationship between the demand and price for an item is given by 2x 6xp 30p 125 000 where x is the number of items demanded each month at a price of p dollars each If the price per item is increasing at a rate of 3 50 per month find the rate of change of the demand with respect to time when the price is 50 per item Interpret your answer Round to the nearest integer if necessary

5 Determine the difference qerotient x h f h where h o for each of the following following function for t

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any 9 6 3 A Q M What is the range Select the correct choice below and fill in any answer boxes within your choice OA The range of the function is y Type an inequality in the form y Use integers or fractions for any numbers in the expression Use comma to separate answers as needed

j f x x 4 x 5 f x h f x h x h 4 x 4 x 5 x h 5 h x 5 x h 4 x 4 x h 5 x 5 x h 5 h

Construct a function that passes through the origin with a constant slope of 1 with removable discontinuities at x 6 and x 4 Enclose numerators and denominators in parentheses For example a b 1 n f x LA sin a 00 E

p f x sin x write as a factor of sin x f x h f x sin x h sin x h h use sin A B sinAcosB sinBcosA sin x cos h 1 sin h cos x h

o f x e f x h f x h x n write the numerator as a factor of e th ex h f x h f x e e e h h

Determine the difference quotient S x h f x h where h 0 for each of the following function 3 x n n

1 For the function F x 5 a graph the rational function using transformations b use the final graph to find the X domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes What is the range of the given function Select the correct choice below and if necessary fill in the answer box to complete your choice O A The range of the given function is yly Type an integer or a simplified fraction B The range of the given function is yly Type an integer or a simplified fraction Use a comma to separate answers as needed OC The range of the given function is yly Type an integer or a simplified fraction O D The range of the given function is the set of all real numbers

4x 5X 9 x 7 00 8x 3x 8x b lim

x u v u 3 x ex 3 6 ubtex xe U ex litur e exx e xe P 3 x V 9 6e p L abe 2ex 6e7 2e 51 J 2 4 1 12x 6e X X 5 be

11 lin NEX 4x 5x 9 8x 3x x

Consider the function p x Select the correct answer below 20 V 1200 32 554 20 V 1200 32 16x 125x What are the critical numbers 5 20 1200 32 20 1200 32

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum Select all that apply Of x ln 1 x over 0 2 Og x ln 1 x over 0 2 h x x 1 over 1 4 0 k x over 1 4 None of the above

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimu Select all that apply Of x x over 2 2 g x x over 1 1 Oh x ln x over 0 3 j x x over 1 1

olve the initial value problem 1 2 A s sint cost 2 C s 2sint 1 21 cost sin t s 3 B s sin t cost 2 D s sin t cost 4

Find the critical numbers of the following function q x 4x x 4x 1 Select the correct answer below 0 A O and 01 02 O There are no critical numbers

Consider the function g x x 3x10 2 Use the second derivative test to find the x coordinates of all local maxima If there are multiple values give them separated by commas If there are no local maxima enter

Given f x x 4x 10 find the x coordinates of all local minima using the seco derivative test If there are multiple values give them separated by commas If there a local minima enter Sorry that s incorrect Try again

Analyze the following graph of f x Select all of the intervals over which the graph of f x is concave up Select all that apply 0 1 1 1 1 00 None of the above T 24

29 Find the second derivative of g x e ln 4x

For the following exercises use logarithmic differentiation to find dy dx 346 y xVx X

341 f x ln 5x 7

5 4 3 2 2 1 1 2 3 4 X The function graphed above is decreasing on the interva 0 The inflection point is at x

1 The function f x 8x critical number X 2 3 X Question Help Video Add Work 2 e 42 has one critical number Algebrically use the derivative to find the

3 The function f x 2x 33x 180x 3 has one local minimum and one local maximum Use derivatives to algebraically find the answer to the question This function has a local minimum at x with y value and a local maximum at x with y value

The function f x 8x 2 e critical number X 41 has one critical number Algebrically use the derivative to find the

Mark the critical points on the following graph 36 30 Clear All 5 4 3 2 1 Add Work 18 12 Draw 0 6 12 18 z 2 7 Dot 3

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 4x 66x 216x 2 1

The price of a condominium is 188 000 The bank requires a 5 down payment and one point at the time of closing The cost of the condominium is financed with a 30 year fixed rate mortgage at 8 Use the following formula to determine the regular payment amount Complete parts a through e below PH PMT 1 1 nt a Find the required down payment b Find the amount of the mortgage Round c How much must be paid for the one point at closing Round to the nearest dollar as needed d Find the monthly payment excluding escrowed taxes and insurance S Round to the nearest dollar as needed e Find the total cost of interest over 30 years as needed K

The function f x 2x 33x 108x find the critical numbers The smaller one is x and the larger one is x Question Help Video POEMENE 2 has two critical numbers Use derivatives to algebraically

An ellipse or hyperbola uses the general form Ax Cy Dz Ey F 0 Solving for 5 unknowns A B C D E F requires 5 equations needs 5 points given But if one of the coefficients is divided out A or C then only 4 coefficients remain and only 4 points are needed x Cy Dr Ey F 0 Given 4 points on a vertical ellipse 1 2 517 0 1 933 1 0 65 and 4 449 0 Select the missing coefficients answers have been rounded to the nearest tenth x y Select Select Select y Select 0 x

Algebraically find the critical numbers of the function f x 4x5 5x 20x 7 and classify them Leave answers in 4 decimal places X X X Add Work is a Neither a max or min is a Neither a max or min is a Neither a max or min

Question 2 6 5 7 4 d The function graphed above has an inflection point Add Work

HER PRACTICE ANOTH Of the infinitely many lines that are tangent to the curve y 8 sin x and pass through the origin there is one that has the largest slope Use Newton s method to find slope of that line correct to six decimal places 10 083850

ASK YOUR TEACHER Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day island 5 km W L B 9 km 1 144 D nest A bird with these tendencies is released from an island that is 5 km from the nearest point B on a straight shoreline flies to a point C on the shoreline and then flies along the shoreline to its nesting area D Points B and D are 9 km apart Assume that the bird instinctively chooses a path that will minimize its energy expenditure Round your answers to two decimal places a In general if it takes 1 2 times as much energy to fly over water as land to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area 1 5 km from B MY NOTES W L b Let W and L denote the energy in joules per kilometer flown over water and land respectively Assuming the bird s energy expenditure is minimized determine a function for the ratio in terms of x the distance from B to C 25 c What should the value of Wbe in order for the bird to fly directly to its nesting area D L X PRACTICE ANOTHER d If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B how many times more energy does it take a bird to fly over water than land 1 144

Find the area of the region bounded by the polar curve r 6e on the interval 2T Answer Granh the curve on a calculator Turn in a sketch of the curve

You would like to have 3500 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4 compounded semiannually Answer parts a and b i Click the icon to view some finance formulas a How much should you deposit at the end of every six months In order to have 3500 in 3 years you should deposit s at the end of every six months Do not round until the final answer Then round up to the nearest dollar b How much of the 3500 comes from deposits and how much comes from earnings S of the 3500 comes from your deposits and comes from interest Use the answer from part a to find this answer Round to the nearest dollar as needed More info In the provided formulas P is the deposit made at the end of each compounding period for an annuity that pays an annual interest rate r in decimal form compounded n times per year and A is the value of the annuity after t years A 9 r nt auon by mar 1 P A rnt A

Analyze the polynomial function f x x x 5 using parts a through h below The last 2 FUNCTIS VI mupiicity z su te graphi vii Roches d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin A B OA Q OB aLA V The gitation the functions of pHCRY SO the graph UNI cusses the axis al x 20 Xmax 20 Xscl 2 Ymin e Approximate the turning points of the graph The turning point s of the graph is are 0 0 3 33 18 52 Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed f Use the information in parts a through e to draw a complete graph of the function by hand Choose the correct graph below O C O C 30 Ymax 30 Yscl 3 Choose the correct graph below O D D is

9 For what angles x in 0 27 does the sin x have the same value as cos 7

K Analyze the polynomial function f x x x 5 using parts a through h below The x intercept s is are 0 5 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The y intercept s is are 0 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the real zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept 4 The real zero s of f is are 0 5 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The lesser zero of the function is of multiplicity 2 so the graph off touches the x axis at x 0 The greater zero of the function is of multiplicity 1 so the graph of f crosses the x axis at x d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 20 Xmax 20 Xscl 2 Ymin 30 Y max 30 Yscl 3 Choose the correct graph below A oo OB O C 2 e Approximate the turning points of the graph The turning point s of the graph is are Type an ordered pair Round each coordinate to the nearest hundredth as needed Use a comma to separate answers as needed OD Q

a Use the appropriate formula to find the value of the annuity b Find the interest Periodic Deposit 90 at the end of every six months iClick the icon to view some finance formulas Rate Time 6 5 compounded semiannually 40 years a The value of the annuity is Do not round until the final answer Then round to the nearest dollar as needed b The interest is Use the answer from part a to find this answer Round to the nearest dollar as needed x m W SO ty is hal a rt a www Formulas In the provided formulas P is the deposit made at the end of each compounding period r is the annual interest rate of the annuity in decimall is the number of compounding periods per year and A is the value of the after t years P 1 0 1 P A 1 A A C P A

To offer scholarships to children of employees a company invests 15 000 at the end of every three months in an annuity that pays 10 compounded quarterly a How much will the company have in scholarship funds at the end of ten years b Find the interest Click the icon to view some finance formulas a The company will have in scholarship funds Do not round until the final answer Then round to the nearest dollar as needed b The interest is S Use the answer from part a to find this answer Round to the nearest dollar as needed Formulas In the following formulas P is the deposit made at the end of each compounding period r is the annual interest rate of the annuity in decimal form n is the number of compounding periods per year and A is the value of the annuity after t years A P 1 0 1 r A P A P 1 r 8 In the following formulas P is the principal amount deposited into an account ris the annual interest rate in decimal form n is the number of compounding periods per year and A is the future value of the account after t years A n nt nt X

Question 6 The polynomial of degree 3 P x has a root of multiplicity 2 at x 3 and a root of multiplicity 1 at x 5 The y intercept is y 18 Find a formula for P x P x Question Help Video Message instructor

Find the value of the annuity and the interest Round to the nearest dollar A nt A P 1 r 1 r A P 9 A nt OA 21 047 3 047 OB 22 420 4 420 C 29 722 11 722 D 62 420 44 420 1 P Periodic Deposit 900 at the end of every six months Rate 4 5 compounded semiannually Time 10 years

At the time of her grandson s birth a grandmother deposits 10 000 in an account that pays 3 5 compounded monthly What will be the value of the account at the child s twenty first birthday assuming that no other deposits or withdrawals are made during this period Click the icon to view some finance formulas The value of the account will be Round to the nearest dollar as needed

Use technology to find points and then graph the function y 2 log x 2 2 following the instructions below done plotting points Plot at least four points with integer coordinates that fit on the axes below Click a point to delete it 74 S