Application of derivatives Questions and Answers

Use the graph of the function to answer each question 2 x 2 f x csc x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

Use the graph of the function to answer each question 2x x 2 f x cot x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

4 AVMN has sides of lengths v n and m a Write an expression for the height of the triangle h in terms of the measures of the sides and angles of the triangle b Write an expression for the area of AVMN V m n N

1 In AACD AC 25 inches and DC 18 inches a Find ED to the nearest tenth b Find the area of AACD D

B Find the area of AMPO Round to the nearest hundredth M 14 66 O P 17 5

Susan is flying a kite which gets caught in the top of a tree Use the diagram to estimate the height of the tree 63 6 ft 1 59 ft 74 2 ft 86 9 ft string 44 90 feet

q The graph of the function f in the figure below consists of line segments and a quarter of a circle Let g be the function given by g x f t dt Determine the following a g 6 sidot art mo Dedi ort ofbmixo quo of almidue Strange 0 toq mawa oy bbw b g 4 de quoy al fotonu palabonont auc c g 8 Sydw Seulov U17 90 885 10 93 653211 6 S910

2 A particle moves along the y axis so that its velocity at time t 0 is given by v t 1 tan et At time t 0 the particle is at y 1 Note tan 1 y arctanx a Find the acceleration of the nesti 1

315 A

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t O and t X for the graph below Evaluate A x for x 1 2 3 and 4 5 4 3 2 1 A 1 A 2 A 3 A 4 2 3 5

6 Co primality Let a b be two integers We call a and b relatively primes or co primes IFF gcd a b 1 Show that the numbers 6k 5 and 7k 6 are relatively prime for every k 1 2 2

5 In ADEF angle F is an obtuse angle Is the value of d x ex cos F positive or negative Explain

A spherical snowball is melting in such a way that its radius is decreasing at rate of 0 1 cm min At v rate is the volume of the snowball decreasing when the radius is 15 cm The volume of a sphere of radius r is V 4 3 The volume is decreasing at a rate of cm min

Find the point x y on the unit circle that corresponds to the real number t t 6 x y 3 2 1 2

S 1 point The function is defined by f z a sin b a c d for constants a b c and d In the y plane the points 2 2 and 4 4 represent a minimum value and a maximum value respectively on the graph of f What are the values of a and d a type your answer d type your answer

point Library Michigan Chap16Sec3 Q47 pg Let W be the solid half cone bounded by z x y z 1 and the yz plane with x 0 and let Let W be the solid half cone bounded by z x y z 4 and the xz plane with y 0 V For each of the following decide without calculating its value whether the integral is positive negative or zero a Jw x y2 dV is positive negative zero b Jw yzdV is positive negative zero c Jw Vx y2dV is positive negative zero

Find if possible the complement and supplement of the angle Enter NONE in any unused answer blanks 5 6 complement

Find the difference of the angles Write your answer in D M S form 120 45 29 and 18 36 6

Convert the angle measure from degrees to radians Round your answer to three decimal pl 47 24 rad

An aqueous solution contains 0 150 M HCI at 25 0 C The pH of the solution is O A 0 82 O B 7 00 O C 0 150 O D 13 00 O E 1 00

A C TC 3 13 cos 1 1 A 73 C 9 15 sin cot A 2 3 B B D TC 3 2 D 3 TU B C 0 D TC In 2 TO 6

graph of the O is Shown in the figure below Which of the following coul be the graph or f 2 E y y f 2 B

Given is the graph of f x Answer the following questions Make sure you justify your answers q Determine intervals where f x is decreasing 10 Determine the x value s of any relative maximum s on the graph of f x 8 7 6 5 3 2 1 2 3

For the table to the right selected values of x and f x are given Assume that f x and f x do not change signs II Is f x increasing or decreasing 12 Is f x concave up or concave down X f x O 3 5 23 8 12

p Given f x x 3e x 0 8 on what intervals is f increasing CALCULATOR

graph of the derivative of in the figure below Which of the to the graph or f 0 y y f X is Shown following could B E

Geometry 5 Find the measure of each indicated angle Favorite Type of Music B a AE b ACE R B 17 A Pop Country H 66 55 C Hip Hop Rap 26 G 89 28 Folk Other F 32 47 Christian E Rock D d BHC e FD c GDC f FBD

x ux 2 CX 232

14 log 4 log 2x 1

8 25 3x 6 125 12 2x

5 logx log4 1

4 7 2log x 3log4

2 Tiana started working at Pax River Ale House earning 9 25 per hour Every six months she gets a 3 25 raise If Tiana has worked at the Ale House for 4 years what is her current hourly rate

3 While skiing last weekend Mr Weisner noticed an ice sculpture that started out at 52 inches tall wa melting continuously at a rate of 3 per minute Find the height of the ice sculpture after 15 minu

5 If tan cot 0 and 0 0 A sin cos which of the following statements must be true B 1 sec 0 1 csc 0 C sin cos 0 1 D None of the above

4 If tan 03 find sec 0

A boat is sailing due east parallel to the shoreline at a speed of 20 miles per hour At a given time the the bearing to a lighthouse is 68 E and 30 minutes later the bearing is 52 E Find the distance from the boat to the lighthouse at Boat Position 2 0 Two planes leave an airport at the same time One plane is flying 650 m p h at a bearing N 37 E and the other plane is flying at 825 m p h at a bearing of N 53 W How far apart are the planes after flying for 2 hours FORS 8

6 1 point What is the IQR of the set of the data below 52 61 71 63 54 69 63 65 68 58 57 11 10 15 000 019

Suppose that 28 000 from a retirement account is invested in a large cap stock fund After 20 years the value is 86 000 Use the model A Pertto determine the average rate of return under continuous compounding Round to three decimal places Avoid rounding in intermediate steps Your Answer

Pertor A P 1 nt to solve the following Use the model A Pertor A problem 45 000 is invested at 3 1 compounded monthly How long will it take for the investment to double Round to the nearest tenth of a year

g x 2 3 d 2 2 x 2 5 10 X

A polynomial of degree 12 may have at most relative extreme values maximums and minimums 12 A roots and at most

1 5 Evaluate sin sin 0 25 and explain your reasoning

17 Hint Draw a right triangle 7 Evaluate sin arccos

3 Kymani was asked to evaluate cos cos His answer and explanation are given below 1 COS cos because the inverse cosine function undoes the cosine function so the output must be the same as the original input Do you agree with his answer and explanation Explain

3 Which of the following pairs of functions have the same range Choose all that apply 1 f x sinx and g x cos x II f x tan x and g x arctan x III f x arcsin x and g x arctan x 1 IV f x cos a and g x sin x

Fill in the blanks Do not rationalize at b e d tan 57 12 11 1 b 3 3 d

Find a b and c Note that the fraction is not simplified sin 57 6 X 1 2

6 y tan 0 A B D 3 2x Z 3x 2 3r 4x

Write Name Date Period Show all work including labeled triangles in the unit circle showing direction 1 Graph y tan x 3TT 2 T TT 2 y 3 2 0 1 2 3 TT 2 TT 3TT 2 X