Application of derivatives Questions and Answers

Calculate the average rate of change of the given function over the given interva Interval 0 2 X f x 0 G 1 2 3 4 5

Verify the following Functions Be sure t 16 sin 1 4 5

Vectors u and v are shown on the graph 10 9 8 7 6 543 24 1 0 PT 7 7 7 4 97 1 Ty 1 NI XA 2 3 4 u 6 7 8 co 9 V 10 11 12 13 14 15 16 17 x Part A Write u and v in component form Show your work 3 Part B Find u v Show your work 2 points Part C Find 5u 2v Show your work 5 points

Drum Tight Containers is designing an open top square based rectangular box that will have a volume of 1372 in What dimensions will minimize surface area What is the minimum surface area What are the dimensions of the box The length of one side of the base is The height of the box is in

Maximize B 2xy where x and y are positive numbers such that x y 10 The maximum value of B is Simplify your answer Type an exact answer using radicals as needed

S O https www webassign net web Student Assignment Need Help Read It 5 7 Points DETAILS Watch It TANAPCALC10 2 6 030 0 6 Velocity of a Ball Thrown into the Air The position functi average rate of change of f over a b its Instantaneous velo A ball is thrown straight up with an initial velocity of 112 ft sec a What is the

Find the smallest positive value of c for which x c is a vertical asymptote for the graph of the function f x 3tan 2 40x Provide 4 decimal places

For what value of k will the function f be continuous on 0 x k f x k 9 X 3 if x 3 if x 3 4

3 XX 1 Name X 0 Linear Exponential Regression The graphs below represent either a linear y ax b or an exponential function ya b Find the equation of the function by using the appropriate regression on the calculator Roond to the nearest hundredth Y 2 1 3 H X 2 Y 6 NWS 0 1 1 33 What if we cannot determine the common difference or common ratio very easily We can find the function equation by regression Use the appropriate regression on the calculator to find the equation of the following functions Round to the nearest thousandth 3 4 5 6 10 14 18 22 1 2 3 4 6 2 19 2 59 582 184 7 4 6 X HEWA Y XX 33 0 0 35 HWR9 1 3 0 1 1 2 3 4 0 7 1 4 2 8 5 6 0 1 2 3 Y 1 5 1 125 0 84375 0 63281 4 0 47461

8 In 1985 there were 285 cell phone subscribers in the small town of Centerville The r subscribers increased by 75 per year after 1985 Don t consider a fractional part of a person Years since 1985 Number of Cell Phone users 1 498 2 872 3 1527 4 5 2672 4677 6 8186 b Use your model to predict the number of cell phones in 1997 c Is this an example of exponential growth or decay 7 14325 8 25069 9 a Determine an equation for a function that models this data set Round to the nearest hundredth 43871

The function f is defined as follows f x 3x 2 if x 0 if x 0 a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range a The domain of the function f is 0 00 Type your answer in interval notation b Locate any intercepts Select the correct choice below and if necessary fill in the answer box to complete y choice OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed B There are no intercepts

Devise an exponential decay function that fits the given data then answer the accompanying questions Be sure to identify the reference point t 0 and units of t The pressure of a certain planet s atmosphere at sea level is approximately 800 millibars and decreases exponentially with elevation At an elevation of 35 000 ft the pressure is one third of the sea level pressure At what elevation is the pressure half of the sea level pressure At what elevation is it 1 of the sea level pressure What are the units of t A millibars B feet C pressure levels At what elevation is the pressure half of the sea level pressure 22083 feet Do not round until the final answer Then round to the nearest whole number as needed At what elevation is the pressure 1 of the sea level pressure feet Do not round until the final answer Then round to the nearest whole number as needed

Solve the equation in the complex number system x 5x 9 0 The solution set is Simplify your answer Type an exact answer using radicals and i as needed Use integers or fractions for any

Solve the equation in the complex number system x 81 0 The solution set is Simplify

Write the expression in the standard form a bi r 3 3 7 8i 0 11 Simplify your answer

Find the quotient and remainder using synthetic division 4x3 16x2 12x 3 X 5 quotient remainder

A certain drug is eliminated from the bloodstream with a half life of 36 hours Suppose that a patient receives an initial dose of 70 mg of the drug at midnight a How much of the drug is in the patient s blood at noon later that day b When will the drug concentration reach 50 of its initial level www a The reference point is midnight If t is measured in hours what is the exponential decay function y t Type an expression Do not round until the final answer Then round coefficients to six decimal places as needed

Find approximate values for x at each of the x values given in the following table Use a right hand approximation where possible If a right hand approximation is not possible use a left hand approximation 0369 12 f x 56 50 38 26 14 x

Two polynomials P and D are given Use either synthetic or long division to divide P x by D x and express the quotient P x D x in the form P x Q x R x D x D X P x 2x 6x 2x 1 D x x 4

Read aloud T a Determine the end behavior b Find the zeros Directions Complete each step and sketch the graph of the poly fractions for some x and y values 1 f x x4 4x 1 c Table of values Choose x values between of 2 8 7 6

2 f x x 3x 4x a Determine the end behavior b Find the zeros c Table of values Choose x values between the zeros

Given the function P t There are at most at most

2 a 8 points Find the Maclaurin series of f x if f 0 0 and f x X 1

Determine whether the following equation is separable If so solve the given initial value problem 2ey y 0 In 5 dx Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution to the initial value problem is y x Type an exact answer in terms of e B The equation is not separable

se the exponential growth function that fits the given data then answer the accompanying question Be s ify the reference point t 0 and units of time population of a town with a 2009 population of 86 000 grows at a rate of 1 9 per year In what year will the ulation double its initial value to 172 000 at is the reference point t 0 A the initial population 86 000 8 the doubled population 172 000 C the rate 1 9 D the year 2009 hat are the units of time A years D decades OG percent D people Write the exponential growth function CITR

The population of a certain state from 2000 to 2010 was recorded During that decade the state grew from 19 4 million in 2000 to 26 5 million in 2010 Use an exponential growth model to predict the population of the state in 2035 Let y t be the population of the state in millions t years after the year 2000 Give the exponential growth function for this state s population y t Type an expression Round coefficients to three decimal places as needed

48 What us the value of sin 45 sin 15 3 1 4 O A A B B 3 1 4 C 1 3 4 D 1 3

47 Find the value of this expression sin 45 sin 15 The second step OA sin 60 sin 30 OB cos 80 cos 30 sin 60 sin 30 C D cos 60 cos 30 co

50 cos 75 cos 15 The value OA B O C O D NA NO 5 2 2 2

9 Express A B OC O D 1 cos 24 as a function of half the given angle 2 cos 48 2 cos 12 4 cos 48 D 4 cos 12

37 Express sin 18 cos 18 as a function of twice the given angle A sin 36 OB co cos 36 OC S D sin 36 Cos 36

1 y graph to 6 4 for the 2 y 6 2 2 4 6 0 3 2 4 6 X

Find the points oo the curee y 2x 3 3x 2 4x 7 with slope 2 that tan s tanges

Question 7 If 0 SHARE 4T 3 D then find exact values for the a sec 0 TRATAMEN b csc 0 c tan 0 d cot 0

Question 8 of 10 Given the trinomial x 2 bx c where both the first and the second signs are negative the signs of the factors will be

Question 6 y values 9876 5 4 327 g x If f x f 3 1 g x h x 2 then 3 x values 4 Out y values the nearest hundredth 5 4 3 2 1 h x 1 x

Use the product rule to answer each of the questions below It is not necessary to algebraically simplify any of the derivatives you compute a Let m w 3w 74 Find m w m w 3w 7 4 In 4 5142 6 x b Let h t sin t cos t t Find h t h t sin t 4 cos t t 4t c Determine the slope of the tangent line to the curve y f x at the point where a 1 if f is given by the rule f x e sin a Start by determining f x f x e sin x cos x 0 f 1 e sin 1 cos 1 d Find the tangent line approximation L x to the function y g x at the point where a 1 if g is given by the rule g x x x 2 g x x x 2x g 1 1 2 L x x 1 2 q X

25 To answer questions 25 27 use the given data Find the values of sine cosine and tangent of angle A in Quadrant III and 0 A 360 cos A 1 2 sin OA OB O C 10 3 10 7 10 OD 3 V10

6 Given tan 24 tan 210 what is the second step equal to 21 1 tan 24 tan21 O A OB O C 1 tan 24 21 1 tan 24 21 tan 24 21 OD tan 24 21

11 Simplify sin 4x cos 3x cos 4x sin 3x A cos x B cos 7x O C sin 7x D sin x

2y 6x 4 0 What is slope of the line that is parallel to the above line O none of these answers 0 6 0 3 3

f x 3x2 2 g x 2x 1 find f x o g x 3 2x 1 2 O none of these answers 2x 1 2 O 3 2x 1 2

Quadratic function f x x 4x 4 is given Using Graphing Calculator how many zeros does it have O it has no zeros O it has one zeros it has two zeros of the

f x x3 4x 3x 2 Find increasing intervals O 45 2 22 O 2 22 inf inf 0 45 2 22 inf none of these answers

f x x3 3x determine if this function is odd or even O it is an odd function none of these answers O it is an even function Oit neither odd nor even function

f x x 4x 3x 2 Find the maximum point O 0 45 2 63 O 0 45 2 63 O none of these answers O 0 45 2 63

ion 1 ph of f x 2 6 2 0 4 answered 8 0 3x 2 in blue together with a tangent line in rec 3 he limit definition the derivative of the function f x x 3x 2 3 then the slope of the tangent line is

Question 6 The graph of y f x is shown below Assume the domain of f x and f x an 154 4 3 p A 4 3 2 1 2 3 0 1 Remember this is the graph of y f x not the graph of y f x Based on this graph y f x is increasing on the interval s y f x is decreasing on the interval s

415 f x x 16 x 3 find the tangent

1 5 4 and 1 5 5 0 3 answered ion 2 T 1998 230 le below gives the annual sales in millions of 1999 2000 2001 2002 20 257 278 293 302 ning the average rate of change of sales is imp