Math Due 03/08 at 10:00 am

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Instructor: Course'

Book: Bittinger: Calculus and Its Applications, 10e

Compute the difference quotient

answer as much as possible.

I for the function f (*) : ----=' Simplifu yourx*9

f(x+h)-f(x) h

f (x+h)-f (x) _ h (x+9)(x+9+h)

-16x*3-

-1

2. Compure the difference quotient

"IJ+-!t for the function f(*) : - 4x2 - 3x_ 2'

Simphfy your answer as much as possible'

f (x+h)-f (x) _

Use the graph to estimate the average rate of change of the percentage of new employees

from 1994 to 2000, from 2000 to 2006, and from

1994 to 2006.

What is the average rate of change of the

percentage of new employees from 1994 to

2000?

Yo Per Year

('l--vpe an int"egerr or a decimal rounded to trvo

decimal places as necded')

What is the average rate of change of the

percentage of new employees from 2000 to

7006?

o/o Pet Yeat

('Iype an integer or a dccimai rounded Io t\^'o

decirnal piaces as neeiled")

What is the average rate of change of the

percentage of new employees from [994 to

2006?

Yo Per Year

(T-vpe an itrteger or a decimal roundeii to two

clecimal piaccs as neecled )

aJ.

0 o

Ernployment

Page 1

Student: Date: j Time:

Assignment: HW 1.3

Instructor: Course:

Book: Bittinger: Caleulus and Its

Utitty is a type of function that occurs in econ;mics. When a con$rmer feceives x units of

a certain produc! a certain amourt of pleasure,

or utility-U, is derived. The follouring is a graph

of a utiiity firnction- Find the average rate of change ofU as x changes &om 0 to 1; &om I to 2; from 2to3; from 3 to4-

Find the average rate ofchange ofU as x changes from 0 to 1'

tr (simptiff your answer.)

Find the average rate of change of U as x

changes from I to 2-

I (si*priff Your answer.)

Find the average rate ofchange ofU as x

changes from 2 to 3.

I (si-priff Your answer.)

Find the average rate of change of U as x

changes from 3 to 4.

[ 1si-prify Your answer-)

Page2

Student: Date: Time:

Assignment: }{W 1.3

Applications, 10e

ia-

Instructor: { Course:

Book: Bittinger: Clalculus and Its Applications, 10e

Suppose that a fashion company determines that the cost, in dollars, of producing x

cellphone-sunglasses is given by C(x): - 0'05x2 + 55x' c(301) - c(300)

r;,ayfrffi.andinterprerthesignificanceotthisresulttothecompany.

c(30l) - c(3oo) rind -- ,['1 _ 369 -. C(301) - C(300) - {Simplify your ansr,ver.)

301 - 300

Interpret the result'

It represents the average cost to produce one item'

It represents the average cost per item to produce 300 items"

It tells us the average cost to produce 301 items'

lt represents the average cost to produce one more item after making 300 items'

Page 3

Student: Date: Time:

Assignment: HW 1.3

6. The home rumge, in hectares, of a carnivorous mammal weighing w grams can be approximated

H(w):0.1lwr'36' a) Find the average rate at which a carnivorous mammal's

horne range increases as the animal's

weight grows from 350 g to 500 g'

H(3oo) - H(2oo) b) Find -ff;ri;-. arrd interpret this result'

a) What is the average rate?

hectares/g

not round until the final answer. Tken round to the nearest hun&edth as needed')

H(3oo) - H(2oo) 300 - 200

iDo uut routrd until the iinal ansll'er. l-iren r6und t3 [he nearest irgnfircdth as needeel')

Interpret the result'

It represents the average home range of a 200 g mammal'

lt represents the difference between the home range of a 200 g mammal and a 300 g

mamrnal.

It represents the average rate of change in the home range tbr a 200 g mammal to a 300 g

mammal.

It represents the average home range of a 300 g mammal'

An object dropped fiom rest from the top of a tall building on Planet X falls a distance d(t) : l9t2

feet in the first t seconds. Find the average rate of change of distance with respect to time as t

changesfromtl:5totz:S.ThisrateisknownaStheaveragevelocity,orspeed' feet

The average velocity as t changes from 5 to 8 seconds is ; (Srrir|liIY 1out ails\\cl J

1,2

Page4

n (Do

InsFuctor: Courser

Book l

Assignment: HW 1.4

Bydeterminingf,(x):I'$ry'lrndf,1z;forthegivenfunction'

f(x) :6x2

f '(7) : [ {si*nliff your answer.)

f(x+h)-f(x) Usef'[x):lim-\'-l h-+o h

to frnd the derivative at x for the given function'

s(x) :4x + 8

s'(x):f

Find an equation fbr the tangent line to the graph of the given function at (2' * 5) '

f(*):*2-g

Find an equation fbr the tangent line to the graph of f(x) : *2 * 9 at (2'- 5) '

v=n

Find the equation of the tangent rine to rhe graph of rix) = 2- u(- t - +)

The equation of the tangent line is y:

Page 1

Student: Date: Time:

lnstructor: Assignment: HW l '4 Course:

Book: Bittinger: Calculus and Its

List the points in the graph in the interval

1 < x < 6 atwhich the function is not differentiable.

Find H'(x) for the given function.

5 H(x): Ix+ 9

n'(*):I (Type an exact answer, using radicais

Thevaluesofxintheinterval I < x < 6at which the function is not differentiable are x: r-ltl. (Use a colnma to separate answers as needed')

as needed.)

PageZ

Student: Date: i Time:

Instructor: Course:

Book: Bittinger: Calculus and Its

Applications. 10e

Assignment: HW l-4

Let f be the following piecewise-defined function'

[*'*B rbrx<5r(x): I Isx+8 forx>5

(a) Is f continuous at x : 5? (b) Is f differentiable at x : 5?

(a) Is f(x) continuous at x: 5?

Yes

(b) Is f{x) differentiable at x: 5?

Yes

Page 3

Student: Date: -

Time:

Instructor: Assignment: HW 1'5 Course:

Book: Bittinger: Calculus and lts Applications. l0e

Find the derivative of f(x) : x3-

r'(") : I dv

Find:. dx

Y:4xe dy_ dx

dv Find -.dx

Y:5x-6 dy_ dx

DitTerentiate.

y:3x3 - l4x2 + 32x+ 2 dyrr dx:LJ

dv Find -.dx

7A v:5x-

dv --:-:l I dxll

Page 1

Student: Date: i Time:

Instructor: Course:

rook: Bittinger: Calculus and lts Applications. l0e

Assignment: HW 1.5

Find the derivative.

f(tr *) g(,V;-:s]:n dx\ x I

finO f'(x).

4xf(*):7

r'(*) : I Find f'(x).

f(x): ( x - 1)

f'(*) : I If f(x) :4xz - 3x * 6, find f'(1)'

f'(1) : [ {smpufy your answer')

If f(x) :{;, find f '(15)- r '(1s) : f

1 dvltrv:*,tino;l x=-2.

dvl . lx= -2 -dxl

1\rrnplill' ) ou!' illlswt'r. )

12. Find an equation for the line that is tangent to the curve Y: x3 * 9x at the point (3'0)'

The equation is Y:

10.

11.

Page2

Studen*' Date: Timer

Instructor: Course:

Assignment: IfW Studentr D*e:317175 Time: 10:18 PM

14.

Book: tilttmgsr: L:alculus and Its Applications, 10e

For the function, find the points on the graph at which the tangent line is horizontal'

,:12 + I

Select the correct choice below and, if necessary, fi1l in the answer box to complete your choice'

i,jA The point(s) at which the slope of the tangent line is horizontal is(are) ffi ' (Tvpe an ordererl pair. lJse a comlrla t0 separate ansrvers as ileei1ed.)

The tangent line is horizontal at all points of the graph'

There are no points on the graph where the tangent line is horizontal.

For the function, find the point(s) on the graph at which the tangent line has slope 6'

y: -0.025x2+2x The point(s) isiare

isirnplifl,,\iour anslver. T5rpe an orderecl pair. {Jse a uornllla t0 scparate afiswers as needed')

The position, s, in meters, of a rock in free fhll near the surface of a certain planet is given by

,(0 : 2.g7t2,where t is the time in seconds. Find the rate of change of the position of the rock with respect to time.

The rate of change in position with respect to time is

15.

Page 3

13.

16.

Assignment: HW 1.5

Book: Bittinger: Cdculus andlts Applications, [0e

The population of a city grows from an initial size of 800,000 to a size P given by

P(t) : 800,000 + 1000t2, where t is in years' dP

a) Find the growth rate, ;- b) Fhd the PoPulation after 15 Yr' c) Find the growth rate at t: 15'

dP a) Find the growth rate, ;.

b) Find the poPulation after 15 1T '

tSirnl',,litr \ iltll tln\\\'Itr ,

c) Find the growth tate at t: 15'

T (Simpliff your answer')

Page 4

Instructor: Course. -

Student: Date: Time:

Instructor: Course:

Book: Bittinger: Calculus and Its Applications. 10e

Use the product rule to frnd the derivative'

y: (Zxz + 5)(ax - 3)

Y,:T

Find the derivative.

4x3+8

Y,:I

Differentiate the function.

y- (3*a-x+2)(-x5+8) y':f Diff-erentiate the fu nction.

2x2*1 v: 7x3+8 v:

5. Find the derivative of the hrnction'

r/'-: fts) _ tr;J

Choose the correct answer below'

i/.({i-z)' 5

'l-' (d,.;f

Aa_

C]D

({u-z)' 5

Page 1

(d*+ z)'

Student: Date: Time:

Differentiate.

F(x): Bx _,

r'(r):I

The cost, in dollars, of producing x jackets is given by C(x) : 938 + tS{;- Find the rate at which the average cost is changrng when 576 jackets have been produced.

Find the rate at which the average cost is changing when 576 jackets have been produced.

dollars perjacket

(Round to four decimal places as needed')

Page2

Student: Date: Time:

Book Bittinger: Calculus and Its Applications, 10e

Differentiate the function'

y: {7 *i dy ,-tt ox

Differentiate the firnction'

1 al:--_

' (5* - l7)' iL: dx

Differentiate the given function'

,: *11a + 1) 3

lt*(*o+t)rl: dx

Differentiate the function'

(3x+4)3 al__--=r

14x + 3;*

dy* dx

The position of a particle moving along a coordinate line is ': i/80

+ 4;' with s in meters and t in

seconds. Find the rate of chang. ortl" particle's position at t: 5 sec.

The rate of change of the particle's position at t: 5 sec is m 1 sec'

(Type an integer or a simplified fraction')

\? Page 1

The total outstanding consumer credit of a certain country can be modeled by

the function

C(x):0.2lxa*5.92x3+50.94x2-18'99x+i133'13'wherexisthenumberofyearssince2000' dC

a) Find -:-.

or u.,r*Tis model. predicr how quickly ourstanding consumef cre<lit wilr be rising in 2011'

dC a)-, :

b) The consumer debt will be rising by $ billion per year in 2011'

(SimplifY Your answer')

Page2 \.,7

l d2y Find --*.

dx'

Y: -9x8-9 .)o-y dx2

2. d2v Find-..

dx'

5xa v:-_7x"4

dry

dl:

d2v Find -- ^ .dx'

Y:6x+ 4

dry

d/ :

Find f '(x).

7 f(x)-6xr-lr*--

f "(*): I Find y ".

45 Y: ) --x-x

ttv :L_l

Page 1 tfi

t ll6. rlno y

,:**

u v

'/. When an object is dropped on a certain earth-like planet, the distance it falls in t seconds, assuming that air resistance is negligible, is given by

s(t): 17tz

where s(t) is in feet" Suppose that a medic's reflex hammer is dropped from a hovering helicopter.

Find (a) how far the hammer falls in 4 sec, (b) how tast the hammer is traveling 4 sec after being dropped, and (c) the hammer's acceleration after it has been falling for 4 sec.

(a) The hammer falls feet in 4 seconds' ( Si rnpl ify 1'our airsr,ver. )

(b) The hammer is traveliag f ru*"" 4 seconds after being dropped' (Simplify your answer.)

Page 2

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