Application of derivatives Questions and Answers

12 What is the period of y 3 sinx a 6 b 3TT C d TT 3 2TT

8 What is the period of the graph of y cos x TT 4 b 2TT a C TT E d os x TT

TT 10 What is the phase shift of y cos x cos x 1 4 a b C F F FIN FIC TT 4 TT 4 to the left to the right to the right t 2 d to the left

a C 4 Which diagram shows one period of the graph of y sin 3x 544 201 5 4 11 b d 54 A A 311 3TT 311 5 15 m 6 TT

5 What is the period of the graph y 2 a 3 2TT 3 b 4TT 3 d 6 C sin 3x sir

3 What are the extreme values of y 2 sin x a TT and TT b 2 and 2TT c 2 and 2 d 1 and 1

2 What is the period of the graph for y 2 sin x a 1 b 2TT C TT d 2

Select the response that best completes the statement or answers the question 1 Which diagram shows one period of the graph of y 2 sin x a C 1 1 24 EN TI TT I 2 TT b d n TT 2TT TI

Kim is trying to decide whether she can afford a loan she needs in order to go to chiropractic school Right now Kim is living at home and works in a shoe store earning a gross income of 1 200 per month Her employer deducts 200 for taxes from her monthly pay Kim also pays 140 on several credit card debts each month The loan she needs for chiropractic school will cost an additional 132 per month Help Kim make her decision by calculating her debt payments to income ratio with and without the college loan Remember the 20 percent rule Enter your answers as a percent rounded to 2 decimal places Ratio with college loan Ratio without college loan Debt Payments to Income Ratio

a 1 fUsec t sec 0 The data for the acceleration a f of a car from 0 to 6 seconds are given in the table above If the velocity at 0 is 11 feet per second the approximate value of the velocity at 6 computed using a left hand Riemann sum with three subintervals of equal length is A B C D E 26 ft sec 30 ft sec 37 ft sec 39 ft sec 41 ft sec

X 1 1 1 2 1 3 1 4 f x 4 18 4 38 4 56 4 73 Let be a function such that f z 0 for all x in the closed interval 1 2 Selected values of fare shown in the table above Which of the following must be true about f 1 2 A f 1 2 0 B D E 0 f 1 2 1 6 1 6 f 1 2 1 8 1 8 f 1 2 2 0 f 1 2 2 0

Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters What is the radius of the one with maximum volume B D 3 cm 10 cm 20 cm 8t cm 10 cm

On the graph of y f x the slope at any point x y is twice the value of x If f 2 3 what is the value of f 3 A B O 7 00 6

x 1 0 1 2 B f x g x 5 1 2 0 0 5 D 10 1 The table above gives values of the differentiable functions fand g and of their derivatives f and g at selected values of x If h x g x what is the slope of the graph of hat x 25 1 f x g x 3 1 0 5 0 1 0 5 2

161 4 cm 161 4 cm m Type an integer o

Convert the quantity to the inc 11 6 L to pints

Fill in the blank with the an appropriate A procedure used to convert from one

Use the meaning of the prefix What does deci mean AUDA 3 fraction or a de

Find the open interval s where the following function is increasing decreasing or constant Express your answer in interval notation 10 5 Enable Zoom Pan 5 44

Work Spring 2023 Question 7 Part 1 of Let f xy 3x By 7 Find the following values of fxy for the given coordinates a f 2 1 1 2 1 Simplify your answer

Part 2 of 2 points O Points 0 c A 6000 seat theater has tickets for sale at 24 and 40 How many tickets shoul serformance to generate a total revenue of 176 000 The number of tickets for sale at 24 should be 4000 The number of tickets for sale at 40 should be

se substitution to solve the system 4x 9y 24 x y 3 elect the correct choice below and if necessary fill in the answer box to complete your choic A The solution is Simplify your answer Type an ordered pair B There are infinitely many solutions C There is no solution

Evaluate the limit lim 12xe 4 using L H pital s rule x48 After applying L H pital s rule the limit becomes fill in a function lim x18 12 4x e X Then the answer is fill in a number lim 12mg 4x

Points 0 of 3 ding to projections through the year 2030 the population y of the given state in year x is approxin State A 5x y 11 200 State B 141x y 6 000 x 0 corresponds to the year 2000 and y is in thousands in what year do the two states have t wo states will have the same population in the year

stion y the elimination method 1 39 points O Points 0 of 1 Select the correct choic fill in the answer box to OA The solution is Simplify your at ordered pair OB There are infinit OC There is no solu

The amount of foreign earnings in trillions of dollars kept overseas can be approximated by the function f x 0 223 121 where x 5 corresponds to the year 2005 Find the first full year in which the foreign earnings kept overseas exceeds the following amounts a 1 6 trillion b 2 2 trillion a The first full year in which the foreign earnings kept overseas exceeds 1 6 trillion is 2011 Type a whole number b The first full year in which the foreign earnings kept overseas exceeds 2 2 trillion is Type a whole number

he cost of producing x teddy bears per day at the Cuddly Companion Co is calculated by their marketing staff to be given by the formula C x 100 41x0 06x a Find the marginal cost function C x C x Use it to determine how fast the cost is going up in at a production level of 100 teddy bears per teddy bear Compare this with the exact cost of producing the 101st teddy bear in The cost is increasing at a rate of b Find the average cost function C and evaluate C 100 in C x C 100 What does the answer tell you per teddy bear The exact cost of producing the 101st teddy bear is per teddy bear Thus there is a difference of

Question 15 4 3 67 BE Part 4 of 5 te amount in billions that the government spents on an ongoing project can be approximated by the x 0 186 1 306 In x where x 2 corresponds to 2002 a What was the amount spent in 2005 and 2010 on the project b If the model remains accurate what is the first full year in which the amount spent o the project exceeds 3 7 billion To find the amount spent in 2005 substitute 5 for x in the function amplify your answer HW Score 89 47 17 points Points 3 of 5 he amount spent in 2005 on the project was approximately 2 3 billion ype an integer or decimal rounded to the nearest tenth as needed find the amount spent in 2010 substitute 10 for x in the function amplify your answer he amount spent in 2010 on the project was approximately 0 72 billion ype an integer or decimal rounded to the nearest tenth as needed

Part 1 of 2 1 6 trillion 2 2 trillion CO Points 0 of 4 mount of foreign earnings in trilions of dollars kept overseas can be approximated by the function f x corresponds to the year 2005 Find the first full year in which the foreign earnings kept overseas exceeds first full year in which the foreign earnings kept overseas exceeds 1 6 trillion is a whole number

Question 15 4 3 67 BE Part 1 of 5 HW Score 68 42 13 of 19 points O Points 0 of 5 he amount in billions that the government spents on an ongoing project can be approximated x 0 186 1 306 In x where x 2 corresponds to 2002 What was the amount spent in 2005 and 2010 on the project If the model remains accurate what is the first full year in which the amount spent on project exceeds 3 7 billion the To find the amount spent in 2005 substitute implify your answer for x in the function

Translate the exponential statement into an equivalent logarithmic statement e3 2958 27 The equivalent logarithmic equation is Use integers or decimals for any numbers the equation

Consider lim ex x x18 a lim 8x x X X 8

ork 2 8 Using Derivatives 2 16 answered on 16 mpany determines that in t months the 9 7 3

Suppose f x and g x have the following values f 4 8 and f 4 5 g 4 1 and g 4 3 Assume all functions are continuous Find the following x 9f x 8 a a 1 lim 3 4 1

Next question Suppose f 5 5 g 5 g 5 1 and that f x g x are continuous for all 3 10 2 f x 3 x 5 g x 2 lim ida Cannot Be Determined

Evaluate the limit using L H pital s rule 5x lim xx 3x 818

QUESTION 1 You are the resident scientist on a ship tasked with on each of the isl

What does the computer give for the solution of the general 2 2 system ax cy p bx dy q

Find the value of sin 2a cos 2a and tan 2a for each of the following 3 a cosa 5 7 b sin a 25

Let f x 3x 2 1 4 16 Find f 0 f 16 Enter answer as an exact value

Based on the following data would Ann and Carl Wilton receive a refund or owe additional taxes Input the amount as a positive value Round your intermediate calculations and final answer to the nearest whole number Tax Information Adjusted gross income Standard deduction Child care tax credit Federal income tax withheld Tax rate on taxable income Refund 46 790 24 000 100 1 870 10 percent

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Question 35 Linear Functions Determining The Equation Give termine the Linear Equation for each of the following situ ercept Form ve the equation of the line passing through the point 42 that is parallel to y 6x 8 ve the equation of the line passing through the point 14 that is parallel to y x 7 ve the equation of the line passing through the point 8 5 that is perpendicular to y 7x

Ross Martin arrived at the following tax information Tax Information Gross salary Interest earnings Dividend income Standard deduction Itemized deductions Adjustments to income 57 595 255 165 Taxable income 12 000 11 350 1 700 hat amount would Ross report as taxable income

How many times larger is a A cubic centimeter is tim Type a whole number

1 O O Choose the correct genus of A spool of thread A genus 1 OB genus 2 C genus 3 OD genus 0

shows information recorded about the location and Th a Determine the altitude in miles b Determine the ground speed in miles per hour

times A cubic meter is Type a whole number

The function f x 2x 30x 2 144x 5 has one local minimum and one local maximum This function has a local minimum at x with value and a local maximum at x with value

Given the function g x 8x 24x 72x find the first derivative g x g x Notice that g x 0 when x 3 that is g 3 0 Now we want to know whether there is a local minimum or local maximum at x 3 so we will use the second derivative test Find the second derivative g x g x Evaluate g 3 g 3 Based on the sign of this number does this mean the graph of g x is concave up or concave down at x At x 3 the graph of g x is Select an answer 3 Based on the concavity of g x at x 3 does this mean that there is a local minimum or local maximum at x 3