Application of derivatives Questions and Answers

6 Find the exact value no calculator cos sin 4 5

If U is the set of all integers and M x x is an integer between 3 and 30 find the complement of set M Which set is the complement of set M A M x x is an integers 3 or 30 OB M x x is an integers 2 or 31 OC M x x is an integer 2 or 31 OD M x x is an integer 3 or 30

7 Find the exact radian answer in pi form cos cos

Decide whether the events are disjoint Being a high school football coach and being under 5 years old www Are the events disjoint The events are disjoint because a person under 5 years old cannot be a high school football coach The events are not disjoint because a person under 5 years old and a high school football coach are two different t The events are not disjoint because a person under 5 years old cannot be a high school football coach The events are disjoint because a person under 5 years old and a high school football coach can t be two different t

F the set of genres with more than 7 million subscribers Choose the correct answer below OA F Sports Comedy Fashion Gossip OB F Sports Comedy News Fashion OC F News Sports OD F Gossip Fiction 1 2 3 4 5 6 News Sports Comedy Fashion Gossip Fiction 21 953 000 19 092 000 13 763 000 12 188 000 4 720 000 4 523 014

In the cost function below C x is the cost of producing x items Find the average cost per item when the required number of items is produced C x 8 2x 10 400 a 200 items b 2000 items c 5000 items a What is the average cost per item when 200 items are produced b What is the average cost per item when 2000 items are produced c What is the average cost per item when 5000 items are produced S

In the figure m is parallel to n and m 44 125 Find the measures of the other angles n 8 7 m 34 6 The measure of 46 The measure of 42 The measure of 48 The measure of 45 0 The measure of 43 The measure of 47 The measure of 41 O

Without graphing determine the vertex of the parabola and state whether the parabola opens upward or downward g x 4 x 6 2 What is the vertex of the parabola Type an ordered pair In which direction does the parabola open O downward upward This quest www

Simplify Assume all variables represent positive real numbers Write an 2 91 9 P 18 m 2p9 9 m 8 Type exponential notation with positive exponents 81 P VER

Multiply 5x x 7x 6 2 5x x 7x 6 5x 35x 30x Simplify you

2 Determine whether the following vector field is conservative on R F 2x 5y Is F 2x 5y conservative on R OA No because equals OB No because O C Yes because OD Yes because TAGER f dy TERTANT SUPERCE of dy f dy f does not equal ag x ay Birth ikustam CARNAL ment equals ROCKA TAPOEDIAETER 208 Camer Sammenber HERREN SURE does not equal D tomun Inger COLOSURNOMAL ag dx Saber fa ag x COL ag ax

Directions Determine the type of conic write th x 2 y 2 14x 6y 57 0

Solve each inequality logio x 5 log10 2x O x 0 x 5 O xx 5 O xx 5 Ono solution Question 14

Write each equation in exponential form log10 0 00001 5 O 10 5 0 00001 O 0 00001 10 5 50 0 00001 10 10 5

Solve each inequality logg 6x 1 x 0 x 0 x10 x

Evaluate each expression log10 0 0001 O 1 0 x 10 0 4 O 0 40 1 0 x 105 Question 8

Graph each function f x 2 log4 x O 34 32 S L 3 2 m He 2 3 S fo w 19 2 3

Solve each equation log3 x 5 log3 3x 25 O x 10 Ox 0 5 Ox 10 O x 15 4

Write each equation in exponential form log32 8 vill 03 32 832 3 1 0 3 192 32 19 2 32 8

Question 10 Find the variance of the probability density function to the n hundredth f x x 3 1 6 3 4

2 For the A lim f x function f x B lim f x C lim x 2 f x x 2 2 x 4 find the limit

Consider the following functions Step 1 of 4 Find f g 1 Answer How to enter your answer opens in new window f 1 5 4 1 1 1 and g 1 3 1 4

What are the zeros for the function y x x 8 x 4 Se 8 4

Find f g 9 for the following functions Round your answer to two decimal places if necessary 2x 5 Answer 11 f x and g x 4 x

A cruise ship maintains a speed of 25 knots nautical miles per hour sailing from San Juan to Barbados a distance of 600 nautical miles To avoid a ropical storm the captain heads out of San Juan at a direction of 26 off a direct heading to Barbados The captain maintains the 25 knot speed for 7 hours after which time the path to Barbados becomes clear of storms a Through what angle should the captain turn to head directly to Barbados b Once the turn is made how long will it be before the ship reaches Barbados if the same 25 knot speed is maintained Barbados 26 San Juan

Owners of a bike rental company that charges customers between 5 and 25 per day have determined that the number of bikes rented per day n can be modeled by the linear function n p 200 8p where p is the daily rental charge How much should the company charge each customer per day to maximize revenue

Adam must fly home to city A from a business meeting in city B One flight option flies directly to city A from B a distance of about 457 2 miles A second flight option flies first to city C and then connects to A The bearing from B to C is N29 3 E and the bearing from B to A is N63 5 E The bearing from A to B is S63 5 W and the bearing from A to C is N78 8 W How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight Adam would receive more frequent flyer miles Round to one decimal place as needed

olve the triangle a 5 b 12 c 13 A 22 6 Round to one decimal place as needed Round to one decimal place as needed B

triangular plot of land has one side along a straight road measuring 362 feet A second side makes a 21 angle with the road and the third side makes a 20 angle with the road How long are t ther two sides G The longer side of the triangular plot is feet The shorter side of the triangular plot is feet Round to the nearest hundredth as needed

Choose the correct graph All graphs are 30 30 by 30 30 Select one a O b O C O d X

Solve the triangle shown to the right Ca Simplify your answer 82 Do not round until the final answer Then round to two decimal places as needed CA 10 Then round to two decimal places as needed

Compute the distance between the points 4 2 8 and 3 1 7 The distance is Round your answer to the nearest tenth

The graph of Ay By Cx D 0 where A and Care positive constants is a Select one O a parabola opening left O b parabola opening right O c parabola opening up Od parabola opening down

Heron s Formula for the area of a triangle in terms of the lengths of its sides a b and c is A s s a s b s c where 1 s a b c Use Heron s Formula and a calculator to find the a area of the triangle The area of the triangle is approximately Round to the nearest whole number as need square inches per inches inches cubic inches 91 in 84 in 35 in

10 5 5 Local minimum value s 10 5 X A 10 mine the value s of the local extrema you identified in the previous step Write DNE for all extrema that do not exist Separate multiple answers wit ry Keyp Keyboard Shor

Calculate the average rate of change of f x 5x 3x on the interval 2 4 O 189 O 143 O 143

Given lim f x 56 and lim g x 4 evaluate lim 3 f x x 8 X 8 x 8L g x f x Olim x 8l g x f x Olim x 8L g x Olim X lim 3 17 6 17 f x 3 11

Evaluate lim substitution O O O x 64 x 4x 3x 4 lim x 64 x 4x 3x 4 x 64 2 x 4x 3x 4 lim x 64 x 4x 3x 4 lim x 64 2 x 4x 3x 4 lim algebraically by simplifying if possible then using direct does not exist 16 5 48 3 48 5

Find the instantaneous rate of change of f x of f x x 8x 1 when x 4 O 8 O 14 O 16 O 16

10 Answer Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate multiple answers with a comma if necessary Local minimum at HA Keypa Keyboard Shortc

Consider the following graph of g x Write a formula for g x that describes the transformations performed on the basic function 10 Enable Zoom Pan KA

Graph the following function by considering how the function has been shifted reflected stretched or compressed

Determine the area of the triangle 11 cm 1 The area is Type an integer 25 cm cm cm

Find the linear approximation of f x x when x 1 C L x 1 x 1 O L x 1 x 1 OL x 1 x 1 OL x 1 x 1

18 If a function is an odd function and x y is a point on its graph then which of the following will als be a point on the graph A 1 x D x y B x E y x C x y

Mark the critical points on the following graph z e 0 4 3 2 1 2 1 6 0 8 0 4 0 4 0 8 1 2 1 6 2 Clear All Draw Dot 1 2 3

What are the vertical asymptotes of the graph of f The vertical asymptote s is are Type an equation Use a comma to separate answers as needed ANWAR I 1 10 8 61 4 2 1 2 3 4 5 6 7 8 9 10 11 2 416 8 10 1 Q Q 5

You throw a ball straight up from a rooftop 90 feet high with an initial speed of 96 feet per second The function s t 16t 96t 90 models the ball s height above the ground s t in feet t seconds after it was thrown During which time period will the ball s height exceed that of the rooftop When will the ball exceed the height of the rooftop O Between 0 and 6 seconds including t 0 and t 6 Between 0 and 6 seconds excluding t 0 and t 6 Between 0 and 7 seconds excluding t 0 and t 7 Between 0 and 7 seconds including t 0 and t 7 O O GCCE

Mark the critical points on the following graph x e 0 4 3 21 1 6 1 2 0 8 0 4 0 4 0 8 1 2 1 6 24 Clear All Draw Dot 2

A sphere is to be designed with a radius of 12 cm Use differentials to estimate the maximum error when measuring the surface area of the sphere if the possible error in measuring the radius is 0 25 cm Hint The formula for the surface area of a sphere is A r 4tr O 75 398 cm O 1809 557 cm O 301 593 cm O 452 389 cm