Chapter 11: 34, 36, 64, 92, 94

Section 12.3: 8, 56

Please check chapter 11 questions and correct that are not correct. Also check chapter 12 question 8 correct if necessary, please provide the solution for question 56

**Provide solution: **Answer the following question; How would you graph and use derivatives within a product life cycle

Solution/Answer:

34. y=x3+5

Y`=3x2

Solution/Answer:

Y=8-x2, at x=1

To find slope of tangent line to the tangent line to the given curve at the given value of x we need to find derivative of function

Y`=-2x

Knowing derivative we can estimate it in a given value of x, if x=1, then

Y`=-2x=-2*1=-2

Thus slope of tangent line is -2

Solution/Answer:

g(t)=(t3+t-2)/(2t-1)5

To find derivative of whole function we need to find derivative of each part

G`(t)=(3t2+1)/(160x4 – 320x3 + 240x2 - 80x)

Solution/Answer:

a)

To find energy consumption in 1990 we should calculate that X=1990-1970=20F(20)=-0.000144*(20)3+0.014151*(20)2+0.1388*20+23.35=20.6344

In 2000 year X=2000-1970=30

F(30)= -0.000144*(30)3+0.014151*(30)2+0.1388*30+23.35=36.3619

In 2008 year X=2008-1970=38

F(38)= -0.000144*(38)3+0.014151*(38)2+0.1388*38+23.35=41.1569

b)

To find average rate of change in energy consumption we need to divide difference between energy consumption by quantity of years between 2008 and 2000(41.1569-36.3619)/(2008-2000)=0.59937

c) To find at what rate energy changed in 2008 we need also to know consumption of energy in 2007

F(37)= -0.000144*(37)3+0.014151*(37)2+0.1388*37+23.35=40.5643

F(38)-F(37)=41.1569-40.5643=0.5926

Solution/Answer:

a)

Revenue in 2006 can be calculated as g(16)G(16)=-0.033741*(16)4+1.62176*(16)3-28.4297*(16)2+216.603*(16)-599.806=19.3176

b)

Revenue in 2008 can be calculated as g(18)G(18)=-0.033741*(18)4+1.62176*(18)3-28.4297*(18)2+216.603*(18)-599.806=3.9343

c)

Rate of change of revenue in 2007 should be calculated using g(17)G(17)=-0.033741*(17)4+1.62176*(17)3-28.4297*(17)2+216.603*(17)-599.806=15.8865

Rate of change is 15.8865-19.3176=-3.4311

Solution/Answer:

8. f(x)=x4-18x2+1

We need to find derivative

F`(x)=4x3-36x

To find it on given interval:

4*43-36*4-(4*(-4)3-36*(-4))=256-144-(-256+144)=112+(-122)=0

** **

:

e

.

Subject | Mathematics |

Due By (Pacific Time) | 01/20/2013 12:00 pm |

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