Application of derivatives Questions and Answers

Perform long division on the integrand write the proper fraction as a sum of partial fractions and then evaluate the integral 12x 24x 1 2x 12x 12x 24x 1 2x dx dx

and 12 6 5 section Is the given ordered pair a solution to the system 6 4 3x y 22 2x 3y 24 O Yes No

Score 7 86 12 9 12 answered Question 11 Below one description one graph and one equation are equivalent Choose the proper set 10 9 8 7 You start with 3 Xbox360 games and each month you buy 2 new games You start with 1 Xbox360 games and each month you buy 3 new games Oy 3x 1 Oy 2x 3 do 10 9 8 7 5 2 3 4 6 7 8 9 p

Question 10 A clothing business finds there is a linear relationship between the number of shirts n it can sell and the price p it can charge per shirt In particular historical data shows that 3000 shirts can be sold at a price of 35 while 10000 shirts can be sold at a price of 14 Give a linear equation in the form p mn b that gives the price p they can charge for n shirts Answer p Round the value of your slope to three decimal places Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer Question Help Video Message instructor Submit Question

Question 9 2 2 19 Part 1 of 6 Find the exact values of the six trigonometic functions for the following angle 45 HW O sin 45 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all dem

Differentiate y 8x 5 tan x

A ladder 20 ft long rests against a vertical wall Let be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall If the bottom of the ladder slides away from the wall how fast in ft rad doe x change with respect to when 8 ft rad 2 3

Need Help ASK YOUR TEACHER DETAILS SCALCET9 3 3 043 MI 9 0 12 Points A ladder 20 ft long rests against a vertical wall Let be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall If the bottom of the ladder slides away from the wall how fast in ft rad does x cha respect to when 8 Submit Anserer D 0 12 Points Find the limit ft rad Read It DETAILS sin 5x lim X10 7x Watch t Master it MY NOTES SCALCET9 3 3 045 MY NOTES PRACTICE AN ASK YOUR TEACHER PRACTICE A

5 0 12 Points 7 3 Suppose f a g b h K M 3 F 3 4 and f 7 Let g x f x sin x and h x cos x Find the following f x

Consider the following figure Find lim S 8 0 d Need Help Submit Answer Disc There is a circular arc of length s and a chord of length d both subtended by a central angle 8 18 0 17 Points d 0 S Read It Watch It DETAILS SCALCET9 3 XP 3 002

Evaluate the integral 2 81 y 81 2 dy y 9

Evaluate 8 3 3 S 8 3 3 dx 64 x 8 3 3 dx 2 64 x 8 3 3 Type an exact answer using and radicals as ne

K Use the graph of the function to answer parts a through f P x 4 x 5 1 a Give the coordinates of the vertex The coordinates of the vertex are 5 1 Type an ordered pair b Give the domain and range What is the domain of P x 0 00 Type your answer in interval notation What is the range of P x 0 1 Type your answer in interval notation c Give the equation of the axis of symmetry Type an equation 10 12

f x 9 5e A List all critical numbers of f If there are no critical numbers enter NONE Critical numbers B Use interval notation to indicate where f x is increasing Increasing C List the x coordinates of all local maxima of f If there are no local maxima enter NONE I values of local maxima D Find the x coordinates of all local minima of f If there are no local minima enter NONE I values of local minima E Use interval notation to indicate where f x is concave down Concave down F List the values of all inflection points of f If there are no inflection points enter NONE values of inflection points G List the horizontal asymptotes of f If there are no horizontal asymptotes enter NONE

Consider the function f x 6x 6 List the values of the inflection points of f If there are no inflection points enter NOM

Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very nearly linear A cricket produces 120 chirps per minute at 70 F an 168 chirps per minute at 80 F a Find the linear equation that relates the temperature t and the number of chirps per minute n b If the crickets are chirping at 153 chirps per minute estimate the temperature in F Round your answer to the nearest degree X F

Express the function F in the form f g Enter your answers as a comma separated list Use non identity functions for f x and g x F x x 5 8 f x g x

Consider a triangle ABC like the one below Suppose that a 37 b 26 and c 36 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If there is more than one solution use the button labeled or A 0 B C 0 or X No solution S

From the graphs of f and g in the figure we find the following Assume that each point lies on the gridlines f g 2 f g 2 fg 2 1 2 10 5 bo g y 10 5 5 10 f 5 10 X

Soda Corporation purchased 2 800 shares of its own 0 50 par value common stock for 165 000 As a result of this transaction the company s stockholders equit OA increased by 163 600 B increased by 165 000 OC increased by 1 400 D decreased by 165 000

a Determine the equation of the line that passes through A 2 5 and is parallel to the line with an equation of 3x 2y 5 b Determine the equation of the line perpendicular to the line 3 having equation y x 6 and passing through the point 4

Use implicit differentiation to find dy dx x 3x y y 8

Exploration 2 2 3 The P x Problem A concept Given integers a b and c such that 0 a b and given P x x x a x b 13 where P x is divisible by x c 1 Find a b and c 2 Is your solution unique Justify your answer 41 64 onl

Find the center of mass of a thin triangular plate bounded by the y axis and the lines y x and y 2 xif 8 12x 2y 6 The plate s center of mass is located at Simplify your answer Type an ordered pair Use integers or fractions for any numbers in the expression

S V y 32 1 5 4 3 2 1 4 2 3 4 S 1 2 3 4 5 Complete an equation for the function graphed above Enter abs x for x

O Question 7 6 5 3 2 6 5 4 3 2 2 NO 3 75 5 6 1 2 3 4 5 S The graph above is a transformation of the function x Write an equation for the function graphed above Question Help Video Message instructor

Question 6 Describe a function g x in terms of f x if the graph of g is obtained by vertically stretching f by a factor of 4 then shifting the graph of f to the right 2 units and upward 7 units g x Af x B C where A B C

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050 approximately 82 4 million Americans will be at least 65 The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond A graphing calculator screen displays an exponential function that models the U S population age 65 and over y in millions x years after 1899 Use this information to solve a d below Click the icon to view the bar graph a Explain why an exponential function was used to model the population data A An exponential function was used because exponential functions are always more accurate than linear functions OB An exponential function was used because the data in the bar graph is increasing more and more rapidly OC An exponential function was used because population is always modeled using exponential functions OD An exponential function was used because there are too many data points to use a linear function b Use the graphing calculator screen to express the model in function notation with numbers rounded to three decimal places f x 0 c According to the model in part b how many Americans age 65 and over were there in 2010 Use a graphing calculator million Type an integer or a decimal rounded to one decimal place as needed Does this rounded number overestimate or underestimate the 2010 population displayed by the bar graph By how much Choose the correct answer below and fill in the answer box to complete your choice Type an integer or decimal rounded to one decimal place as needed OA The rounded number overestimates the 2010 population by OB The rounded number underestimates the 2010 population by million million I d According to the model in part b how many Americans age 65 and over will there be in 2020 ExpReg y a b x a 3 500502606 b 1 022918115

26 g u 2u 3u b C 28 y ae V 30 u 2 73 32 ye 1

18 y x 20 f t t 1 t 22 y x x 1 24 y x 2 x

25 y 47 27 y ax bx c 1 13 29 v 1 31 z A Bey

Find the centroid of the region in the first quadrant bounded by the x axis the parabola y 8x and the line x y 6 The coordinates of the centroid are x y Simplify your answers Type an ordered pair Type simplified fractions

17 G x x 2et 19 F x x 5 21 g x x 23 y 1 x x 4x 3

Question 3 For the following exercise describe how the graph of the function is a transformation of the graph of the original function f y f x 6 8 Horizontal shift Vertical shift units Select an answer and unit Select an answer Question Help VIDEO Post to forum Submit

The velocity of a parachutist during free fall is f t 65 1 e 0 15t meters per second Answer the following questions using the graph Recall that acceleration is the derivative of velocity a What is the approximate velocity when t 8 seconds m sec b What is the approximate acceleration when t 0 m sec c Approximately when is the parachutist s velocity 50 m sec seconds d Approximately when is the acceleration 5 m sec seconds Ay 70 60 50 40 30 20 10 0 0 f 10 20 30

Find the coordinates of the relative extreme point of the given function and determine if the point is a relative maximum point or a relative minimum point f x ex 9x The coordinates of the relative extreme point are Type an ordered pair Type an exact answer Is the point a relative maximum point or a relative minimum point relative maximum point relative minimum point

Differentiate the following function f x e x 6 Choose the correct setup below to start differentiating the function OA 3x 6 x e d O B x 6 x e dx dx O C d dx OD dx d d x 6 6 e3x e6 dx 3x 6 x 6 dx dx d dx e x 6 3x 6 dx

Differentiate the function y In 2x 2x 9 y

f x 1 In x 5 What can f x 1 In x 5 OA In x 5 6 OB In x 5 be rewritten as C In x6 5 OD In x 5 1 Which derivative rule should be applied first d O A The chain rule f g x p h x h x p x h x p x h x h x OC The power rule if p x x for any number r then p x x 1 d OD The product rule p x h x p x h x h x p x B The quotient rule d p x dx h x

4 2 y x 5 17 1 4 r 3 V r 3 9

9 Y t 6t

x r 8 1 2 4

The current toll for the use of a certain toll road is 2 75 A study conducted by the state highway department determined that with a toll of p dollars q cars will use the road each day where q 60 000e 0 4p Is demand elastic or inelastic at p 2 75 To determine if demand is elastic or inelastic the elasticity must be computed To compute the elasticity of demand for the given equation use the formula for elasticity What is the formula for elasticity pf p OA E p f p O OC E p B E p pf p f p D E p pf p f p pf p f p 0 4p Notice that f p q 60 000e is given in the problem statement but f p is not Calculate f p 60 000e 0 4p d f p

1 f x 186 5 2 f x 5x 1 2 3 f x x 3x 4

Find a center of mass of a thin plate of density 8 6 bounded by the lines y x and x 0 and the parabola y 2 x in the first quadrant x 0 y 0 Type simplified fractions

Suppose that f x 3x 1 and g x 2x 9 a Solve f x 0 c Solve f x g x b Solve f x 0 d Solve f x g x e Graph y f x and y g x and find the point that represents the solution to the equation f x g x a For what value of x does f x 0 1 3 Type an integer or a simplified fraction b For which values of x is f x 0 X Type your answer in interval notation Use integers or fractions for any numbers in the expression c For what value of x does f x g x x 2 Type an integer or a simplified fraction d For which values of x is f x g x

5 The radius of a spherical ball is increasing at a rate of 2 cm min At what rate is the surface area of the ball increas ing when the radius is 8 cm

6 Find the slope of the tangent at the given point f x 3 X at x 4 K3

As always show you work all relevant steps any formulas used correct use of good mathematical form and clearly indicate your answers Use skills appropriate to this chapter Circle the correct letter no work required for Multiple Choice 1 The function y has no limit at what value x 1 x 1 a x 1 b x 0 c x 1 K2 d none of the above

Let R be the flow rate of a gas through a cylindrical pipe for a fixed drop in pressure between the two ends of the pipe For the following recall that you do not need to simplify or expand any of your expressions a Find a formula for R r if the flow rate is proportional to the fourth power of the radius R Use k for any constant of proportionality you have in your equation 3 b If R 420 cm s in a pipe of radius 3 cm for a certain gas find a formula for the rate of flow of that gas through a pipe of radius r cm R cm s c What is the rate of flow of the same gas through a pipe with a 4 cm radius R cm s correct